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COPYRIGHT DEPOSIT. 













OHIO STATE UNIVERSITY 
CIVIL ENGINEERING PUBLICATIONS 
NUMBER THREE 


DESIGNING AND DETAILING 

OF SIMPLE 

STEEL STRUCTURES 

BY 


CLYDE T. MORRIS, C. E. 

PROFESSOR OF STRUCTURAL ENGINEERING, OHIO STATE UNIVERSITY 
ASSOCIATE MEMBER OF THE AMERICAN SOCIETY 
OF CIVIL ENGINEERS 


FIRST EDITION 


l * ° > 

j > 

* 


COLUMBUS, OHIO 
1909 




V 



I 


COPYRIGHT 1909 
BY 

CLYDE T- MORRIS 



• « 
< I 
• 9 I 


THE HANN 1 ADAIR PRINTING CO., COLUMBUS, OHIO 




7c 


/ ' 

y 


L13RARY of CONGRESS 

i Two Copies Received 

MAY 5 1009 

- oopynent tntrv 

)Sj no*} 

CLASS CL, KXc* No. 

Z36 Z-J2- 

! COPY B. 





PREFACE 


The object sought in this book is to collect from the many 

i 

larger and more exhaustive works on structural steel design, 
those parts which are applicable to simple structures, and which 
can be taken up in technical schools in the limited time usually 
allotted to the subject: and at the same time, to show by general 
cases and specific examples how the simple laws of statics may 
be applied to the details of steel structures with the object of 
producing details which are in accord with the stresses they have 
to transmit. 

It is presumed that the student has already finished a course 
in stresses, and little time is given here to the methods of calcu¬ 
lating the primary stresses in structures. 

An effort has been made to make the nomenclature, through¬ 
out, conform to that used in “Stresses in Structures by Prof. 
A. Ft. Heller, and a table is given so that the meaning of any 
letter or character in any formula can be at once determined by 
reference to it. In some cases where reference is made to an¬ 
other book, and a formula is taken bodily from it, the nomen¬ 
clature of the original author is retained and the meaning of the 
letters given in connection. 

Cross references to other articles in this book are indicated 
by figures in parentheses giving the article number, thus (14). 
References to other works on the subject are given in foot notes. 

The author wishes to acknowledge his indebtedness to Mr. 
C. C. Heller for the privilege of using various manuscript notes 
and sketches, left at his death by Prof. A. H. Heller, which have 
formed the basis of many of the 'articles in this book. 

It is hoped that by the illustrations given and the methods 
employed, the reasons will be made apparent for many of the 
details commonly employed in structural work, and which are 
many times put in by “rule of thumb 7 ’ and too often without 
due consideration of the stresses they have to carry. 

Clyde T. Morris. 

Columbus, 0., April 6, 1909. 

in 



TABLE OF CONTENTS 


PAGE 

Chapter I—Riveting . 1 

Art. 1 Dimensions of Rivets. 1 

Art. 2 Rivet Holes . 2 

Art. 3 Driving Rivets . 3 

Art. 4 Theory of Riveting. 4 

Art. 5 Requirements for a good Riveted Joint. 9 

Art. 6 Proper Sizes of Rivets. 9 

Art. 7 Spacing of Rivets. 10 

Art. 8 Kinds of Joints. 12 

Art. 9 Design of Riveted Connections. 13 

Art. 10 Examples of Riveted Joints.. . 15 

Art. 11 Net-sections of Tension Members. 20 

Art. 12 Eccentric Stresses in Riveted Connections.... 25 

Art. 13 Showing Rivets on Drawings. 28 

Chapter IT—Designing and Estimating . 29 

Art. 14 Kinds of Structural Steel Work. 29 

Art. 15 Kinds of Shops . 30 

Art. 16 Proposals and Contracts . 30 

Art. 17 Designs and Estimates. 31 

Art. 18 Time Savers . 35 

Art. 19 Order of Estimating . 37 

Art. 20 Specifications . 41 

Art. 21 Stress Sheets and General Plans. 42 

Chapter III—Manufacture and Erection . 44 

Art. 22 Shop Operations . 44 

Art. 23 Erection . 45 

Art. 24 Drafting Department . 46 

Art. 25 A Draftsman’s Equipment. 47 

Art. 26 Ordering Materials . 51 

Art. 27 Shop Drawings . 54 

Art. 28 Order of Proceedure for a Pin-Connected 

P»ridge ..#. 62 


Art. 29 Order of Proceedure for a Plate Girder P»ridge 65 

iv 

































TABLE OF CONTENTS 


Y 


PAGE 


Art. 30 Shop Bills . 67 

Art. 31 Shipment . 69 

Art. 32 Materials . 70 

Art. 33 Inspection . 75 


Chapter IV—Roofs . 

Art. 34 Construction . 

Art. 35 Roof Coverings . 

Art. 36 Types of Trusses .... 
Art. 37 Building Construction 

Art. 38 Loads . 

Art. 39 Stresses . 

Art. 40 The Design of a Roof 
Art. 41 The Detail Drawings 


77 

77 

77 

78 
80 
81 
84 
84 
91 


Chapter V—Plate Girder Bridges . 99 

Art. 42 Construction and Uses. 99 

Art. 43 Stresses in Girders . 99 

Art. 44 The Web.100 

Art. 45 The Flanges .102 

Art. 46 Economic Depth .103 

Art. 47 Stiffeners . 105 

Art. 48 Web Splices .106 

Art. 49 Flange Riveting .107 

Art. 50 Flange Splices .110 

Art. 51 Design of a Stringer.110 

Art. 52 Design of a Deck Plate Girder Bridge.115 

Art. 53 Through Plate Girders . 137 


Chapter VI—Pin-Connected Bridges .139 

Art. 54 Construction .139 

Art. 55 Types of Trusses.139 

Art. 56 Loads . 440 

Art. 5T Tension Members . 141 

Art. 58 Compression Members .142 

• Art. 59 Lateral Systems .146 

Art. 60 Design of a Pin-Connected Railway Bridge. . .146 

Art. 61 Dead Load .147 

Art. 62 The Depth .147 





































TABLE OF CONTENTS 


PAGE 

Art. 63 Stresses .148 

Art. 64 Design of Tension Members .150 

Art. 65 Design of Compression Members .154 

Art. 66 Design of the End Posts .159 

Art. 67 The Portal Bracing .163 

Art. 68 Design of Floor Beams .165 

Art. 69 Top Lateral Bracing . 169 

Art. 70 Bottom Lateral Bracing .170 

Art. 71 Shoes and Rollers.171 

Art. 72 Estimate and Stress Sheet.173 

Chapter VII — Details of Pin-Connected Bridges .177 

Art. 73 Pins .177 

Art. 74 Calculation of Pins .178 

Art. 75 Details of a Riveted Tension Member.182 

Art. 76 Location of Pins in Top Chord and End Post. .185 

Art. 77 Lacing of' Compression Members.187 

Art. 78 Details of the Floor Beams.190 


















N OTATIO N 


A ==total area of cross-section (square inches). 

^/r=net area of one flange. 

An —gross area of cross section of web=th. 
r/=distance shown in the figure. 
b=distance shown in the figure. 

(7—Centrifugal force per pound. 

C C x C 2 C' etc.=Constants of integration. 
c=distance shown in figure. 

7)r=direct stress. 

D.L.=dead load or dead load stress. . 
d=distance from neutral axis to a parallel axis. 

=depth between centers of gravity of the flanges of a girder. 
=depth between centers of chords of a truss. 
f?=Modulus of elasticity. 
e=distance shown in the figure. 

—eccentricity of application of load. 

//=horizontal reaction. 

/>=depth of the web of a girder, (inches). 

/=Moment of Inertia. 

distance shown in the figure. 

Aq=distance between centers of bearings at the top of post. 
7»: 2 =distance between centers of bearings at the bottom of post. 
7v=total length. 

L.L .—live load or live load stress. 
l x 1. 2 etc.=partial lengths. 

3/=moment about any point or bending moment. 

,Y=number of panels. 

P=coneentrated load or force. 
p=panel length. 

P=reaction. 

=resultant of two or more forces. 
r=radius of gyration. 

$=shear. 

5 —unit stress. 

s 1 =m i aximum unit stress in extreme fiber. 

vll 





Vlll 


NOTATION 


s c =unit stress in compression^— 

s,>=dead load unit stress. 
s L =live load unit stress. 
s t =unit stress in tension. 
s w =working unit stress. 

thikness of web of plate girder. 
l 7 =vertical reaction due to horizontal forces. 
n=distance perpendicular to the neutral axis. 

W=total uniform load. 

*r=load per foot. 

£=angle shown in figure. 

=Angle with the vertical made by a diagonal truss member. 





CHAPTER I. 
RIVETING. 


Rivets are used not only to connect members of riveted 
structures together, but also in all sorts of steel structures, to 
join parts of members built up of plates, angles, channels, etc., 
and for connecting details, such as pin plates, lacing bars and 
batten plates. 

1. Dimensions of Rivets. Rivets are made in a machine, 
which upsets one end of a hot bar of steel or iron, forming the 


i 

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1 



SN j, 

f f ~ 
<5 / 

± Zj 


^30.-/ 

I / 

7 


<- 


d 


\ 

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1 _j _f 


'<3>o°/ ^ ea d, and cuts off enough of the 
bar to fuake a rivet of the de¬ 
sired length. 

The size of a rivet is desig¬ 
nated by the diameter of the 
shank, and its length under 
head, thus % in* x 3^4 in. 

_i_j “Button heads/’ which are 

Fi§ - 1 - hemispherical are used where 

there is room for them. Their size depends upon the diameter 
of the rivet. Fig. 1 shows about the proportions which are used 
in structural work for “button heads” and countersunk rivets. 

Fig. 2 gives the standard heads used by The American 
Bridge Company. It will be noted that the heads do not have 
spherical surfaces before driving. The cups on the riveting 
machine are supposed to have hollow spherical surfaces, so that 


23 uffon Heads 


3 


CV-Ue 


,, H&a > 


i 


f 




jr - ' C oanferaanA 

ZS" 

hsa d~>\ 

U-i 


fh 




Heads 

0^0 X—7 ~t|o 






* 


American Bridge Company’s Standard Rivets. 

Fig. 2. 


the pressure will at first be concentrated on the center of the 
head when the rivet is being driven. This aids in upsetting the 
body of the rivet so that it will fill the hole. 

The grip of a rivet is equal to the sum of the thicknesses 
of the pieces joined. The distance between the heads of a rivet 




























I 


2 RIVET HOLES. Art. 2 

will usually exceed the grip, on account of the roughness of the 
surfaces of the parts joined. Allowance is made for this in the 
length of the rivet used, which must be long enough so that 
there will be sufficient metal to fill the hole and form the head. 
A table of lengths required for different grips is given in the 
hand-books published by the various steel companies. (See 
Cambria, page 337J. 1 

2. Rivet Holes. Holes for rivets are either punched , 

sub-punched and reamed or drilled. When 
reaming is required, the amount varies 
with different specifications from % in. to 
14 in. That is, the diameter of the hole 
punched is from % hi., to y± in. smaller 
than the finished hole. The object of 
reaming is to remove the material sur¬ 
rounding the hole which is more or less injured in punching, 
and to insure a better fit and matching of holes. The injury 
done in punching is greater in thick material than in thin, and 
in medium steel than in soft steel. Hard steel is seldom used 
in structural work. 

Where metal is used of greater thickness than the diameter 
of the rivets, it is usually drilled. Also some specifications re¬ 
quire that all holes shall be drilled in certain cases. 

The common practice is to use “punched work” for build¬ 
ings and ordinary highway bridge work, with both soft and 
medium steel. For railway bridges the practice differs very 
much on different roads. Usually soft steel over % in. thick, 
and all medium steel is required to be reamed. It is probable 
that the development of manufacture will be toward drilling all 
holes, which would assure a fit and matching of parts which 
cannot be attained with punched work. Even if it were possible 
to do punching accurately, the matching of 
holes would be difficult to attain because 
punching causes a piece to stretch, and the 
amount of stretch depends upon the thick¬ 
ness of the metal >and the number of holes. 

For this reason, as shown in Fig. 4, it' is 
necessary to ream all holes after the pieces are assembled, so 



Fig. 4. 


Punch y 
L 


*- / /" 
d *-/6 

JpLafe. 


D/e 




Fig. 3. 


J A11, references are made to the 1907 Edition. 

























Art. 3. 


DRIVING RIVETS. 


3 


that the rivets may be entered. This is usually done with a hand 
pneumatic reamer. This reaming does not produce “reamed” 
work, as only part of the injured metal around the hole is re¬ 
moved. Forcing round tapered pins, called “drift pins,” into 
the holes with sledges, instead of this reaming, is not allowable 
because it injures the metal. 

3. Driving Rivets. Rivets are driven hot, and may be 
driven in three ways; by power riveting machines, by pneumatic 
hand hammers, or by hand. Wherever it is practical, rivets are 
driven by power riveters, because these produce better residts 
at a less cost. 

Power riveting machines are of two kinds, direct and in¬ 
direct acting. The direct acting are the most satisfactory, as 
the full pressure may be held on the rivet as long as desired. 
In these machines the ram moves in the line of the final pressure 
throughout the stroke. In the indirect acting machines, the cups 
are held in jaws which are pivoted in the middle, the power being 
applied at one end of the arm and the rivet driven at the other. 
This causes the cup to rotate in the arc of a circle. Consequently 
the cups must be changed every time the grip of the rivet 
changes or else a lop-sided rivet head would result. 

Machines using compressed air are the commonest, and are 
called air riveters. They are used as portable machines, being 
hung from cranes running on overhead tracks in the shop, and 
do very good work if of proper capacity and if the air pressure 
is sufficient. A shop doing girder work should have a machine 
which will exert a pressure of from 50 to 60 tons. Hydraulic 
machines are the simplest and most reliable, but they must be 
used as stationarv machines. Steam machines are also station- 
ary, and these machines 'are therefore better adapted to riveting 
light pieces than large and heavy ones. 

Rivets which must be driven in the field are usually driven 
by hand, but on large jobs power is sometimes used. There are 
generally a few shop rivets in every structure which cannot be 
driven by machine without taking the piece back, after an inter¬ 
mediate operation, like planing, has been performed. Such 
rivets are also usually driven by hand or with pneumatic hand 
hammers. 

The use of the pneumatic- hammer reduces hand riveting to 


4 


DRIVING RIVETS. 


Art. 3 


very small proportions. This hammer strikes very rapidly. The 
blows are comparatively light ones, but very good rivets can be 
driven with it. Pneumatic hammers are often used for field 
riveting. 

Rivets driven by power riveters or pneumatic hammers, 
through several thicknesses of plates, which are then planed 
off to the center of the rivet, will show so tight that it is difficult 
to see the line of demarkation between the rivet and the plates. 

In hand riveting the end of the shank is hammered with 
hand hammers until it is upset roughly into the form of a head. 
A “snap,” which is a hammer with a cup shaped face, is then 
held over it and struck with a sledge until the head is properly 
formed and the rivet is tight. The rivet is held in place while 
being driven by a “dolly,” which is a steel bar with a cup 
shaped face which fits over the head of the rivet. 

The heating of rivets is important, because overheating, or 
“burning” is injurious, as well as doing work on them at a 
“blue heat.” The range of temperature at which wrought iron 
may be worked without injury, is greater than for steel, and 
therefore some specifications require that field rivets shall be of 
wrought iron. If a rivet is not properly heated it is almost 
certain to be a bad one. There are also times in a shop, when 
there is an unusual demand for power, and the pressure used 
for driving the rivets runs too low. 

A loose rivet may be discovered by striking the rivet head 
a sharp blow with a light hammer specially made for the pur¬ 
pose. An experienced inspector can detect loose rivets by the 
jar on the hand and the sound produced, even when no move¬ 
ment can be seen. Sometimes attempts are made to deceive 
inspectors by caulking the heads of loose rivets or by giving them 
several sharp blows with the riveting machine. 

4. Theory of Riveting. In.spite of their importance, there 
is no rational working theory for designing riveted joints and 
connections under stress. Therefore certain assumptions are 
usually made, which ordinarily render the design of riveted con¬ 
nections a very simple matter. 

In a steam boiler or standpipe 1 the important point is to 

Tor the design of standpipes, see Johnson’s u Modern Framed 
Structures Chapter XXVII. 



Art. 4. 


THEORY OF RIVETING. 


5 


get a maximum efficiency of the .joint, which requires that we 
have the same factor of safety in the net sections as in the 
rivets. This subject will not be considered here. In steel build¬ 
ings and bridges it is simply a question of having, at any point, 
a sufficient number of rivets and a sufficient net area to take 
care of the stress at the point. 

The following assumptions are made in designing riveted 
join ts: 

1. That all rivets completely fill the holes into which they 
are driven. 

2. That the rivets in a compression member take the place 
of the metal punched out, but that in a tension member the 
section is weakened because the net section through the rivet 
holes is less than the gross section. 

3. That a rivet cannot safely carry a tensile stress, that is 
a stress pulling against its head. 

4. That the friction between the parts joined should be 
neglected. 

5. That the bending stress in the rivets may be neglected. 

6 . That the net section of a piece of steel will offer the 
same resistance per square inch as the gross section. 

7. That the stress is equally distributed over the net sec¬ 
tion of the pieces joined in tension. 

8 . That the stress is equally distributed over all the rivets 
of a joint. 

These assumptions are largely interdependent and will be 
considered in detail. 

If a rivet were perfectly driven, and the hole completely 
filled when the rivet was hot, it would contract in diameter in 
cooling. This contraction precludes an intimate contact between 
the rivet and the walls of the hole. 1 

Regardless of this fact it is'the universal practice to propor¬ 
tion compression members for gross section, and tension mem¬ 
bers for net section. An allowance should, however, be made in 
compression members, for open holes, or holes for loose fitting 

« 

According to experiments by M. Considere in 1886, the space 
between the rivet and the side of the hole, varies from 0.002 to 0.02 
inches. See Bulletin No. 62 American Railway Engineering and Main¬ 
tenance of Way Association, page 140'. 



6 


THEORY OF RIVETING. 


Art. 4 


bolts or pins. The allowance to be made in tension members 
will be treated in Art. 11. 

Coincident with the contraction in diameter while cooling, 
the length between heads tends to decrease, and a tensile stress 
is set up in the rivet. In addition to this stress, the metal which 
is being riveted together is compressed by the enormous pressure 
exerted by the riveting machine, and w r hen this pressure is re¬ 
lieved, the metal tends to resume its unstrained form, and exerts 
a tensile stress on the rivet. This initial tension tends further 
to reduce the diameter of the cold rivet and cause a greater 
clearance between the rivet and the walls of the hole. The 
amount of the initial tensile stress on the rivet is a very uncer¬ 
tain quantity. It sometimes requires a very little pull on the 
head of a rivet to break it off. This is probably in part due to 
the heat treatment which it has received, making it non homo¬ 
geneous. Nearly all specifications prohibit the use of rivets in 
direct tension, but they are nevertheless so used in certain con¬ 
nections, because the construction is usual and simple. In these 
connections there are usually stresses acting at right angles to 
each other, such as a shearing and a tensile stress. Bolts might 
be used to take the tension and rivets to take the shear, but rivets 
are generally used throughout. 

Experiments indicate that the clearance between the rivet 
and the walls of the hole, allows a slip to take place when the 
friction between the parts is overcome. 1 Therefore friction is 
the resisting force in a riveted joint, so long as the stress is not 
great, enough to produce slip. With good riveting and ordinary 
working stresses there is probably no slip, 2 nevertheless rivets 
are calculated to resist shearing off. If a proper working stress 
is used, the shearing strength of a rivet is a proper measure of 
the friction produced, because the friction depends upon the 
tension in the rivet, and that, as well as the shearing strength, 
depends upon the area of the cross section. In good work the 


J See Johnson’s “Materials of Construction,” Article 375, also 
pages 3 and 4 of Bulletin No. 62 American Railway Engineering and Main¬ 
tenance of Way Association. 

Experiments indicate that slip occurs at a stress of from 11500 
lbs. to 21900 lbs. per sq. in. of rivet cross section. 



Art. 4. 


THEORY OF RIVETING. 


7 


slip is so small that a joint may safely be strained beyond the 
slipping point, if the stresses do not alternate in direction. 1 

Practically, it is considered of great importance, that the 
rivets should completely fill the holes into which they are driven. 
Since this is impossible it is not of so much importance so long 
as sufficient friction is produced between the parts joined. As 
it requires great pressure to make a hot rivet fill the hole, espec¬ 
ially when the holes in the parts joined do not come exactly 
opposite to each other, (see Fig. 4) this pressure is useful in 
bringing the parts into intimate contact, which is necessary to 
develop the friction. 

If no slip occurs, the only bending stress in a rivet is due to 
elastic deformation, if any at all occurs. The longer the rivet 
the less the bending stress. Usually specifications require that 
the grip of a rivet shall not exceed from four to five times its 
diameter, on the supposition that the rivet transmits the stress. 
This requirement is necessary, because if the grip is great and 
the number of pieces to be riveted together is large, the pressure 
exerted by the riveting machine is not sufficient to bring the 
pieces into intimate contact and thus develop the friction. 

When rivet holes are punched, some of the material imme¬ 
diately surrounding the hole is injured, also a riveting machine 
exerts an enormous pressure on the metal near the rivet, and 
may overstrain it. These might tend to reduce the permissable 
unit stress in tension on the net section," but experiments show 
that where the section is suddenly reduced, as in a notched bar 
or in a section through rivet holes, the ultimate strength per 
square inch is increased by an amount which will more than 
^qual the reduction due to injury. 3 

If then the distribution of stress over the net section 
through the rivet holes is uniform, as per the 7th assumption, 
there is no reason why the allowable intensity of stress should 
not be as great as for a section without rivet holes. If, however, 


'See Bulletin No. 62 Am. Ry. Eng. & M. of W. Assoc., pages 3 & 4. 

2 See Proceedings of the Institute of Mechanical Engineers, August 
1887, page 326. 

3 See Proceedings of the Inst, of Mech. Eng., October, 1888, also 
see Heller’s “Stresses in Structures,” Art. 13. 




8 


THEORY OF RIVETING. 


Art. 4 


the stress is unequally distributed, the maximum intensity will 
be greater than the 7th assumption will give. 

There are a number of causes producing non-uniform dis¬ 
tribution of stress over the net section through rivet holes. If 
two plates in tension be joined by several rows of rivets, and 
there is no slip, the stress is transmitted from one to the other 
by means of the friction at their surfaces of contact. This 
friction is greatest under the rivet heads, because the friction is 
produced by the tension in the rivets. Therefore the intensity 
of stress is greater under the rivet heads than half way between 
them. If the stress is tensile in the plates joined, the uniform 
distribution of stress will be interfered with, as in a notched 
bar. 1 

The 'result is, no doubt, a somewhat greater intensity of\ 
stress near the rivet holes than half way between them. 

If the stress is not equal on all the rivets in a cross section, 
as per the 8th assumption, there may be a large variation in in¬ 
tensity of stress over the section. On this account the rivets in 
a joint should he symmetrically disposed about the center lines 
of stress , and eccentric stresses avoided wherever possible. If 
any of the rivets are defective, the result may be the same as 
that of an unsymmetrical distribution. 

If the friction which is produced by the rivets is greatest 
under the rivet heads, the stress is transferred from one plate 
to the other in a series of increments. The stress in one plate 
increases, while that in the other decreases. The result is that 
the intensity of stress in the two plates at a cross section is not 
equal, and this tends to cause one plate to deform more than 
the other and thus throw more stress on the rivets at one end of 
the joint in one plate and upon those at the other end in the 
other plate. But the plates cannot deform unequally as long 
as there is no slip, so there is no reason why there should not he 
a uniform distribution of stress over the rivets , as long as they 
are all in the same condition. This would require perfect work¬ 
manship. 


*See Proceedings of the Inst, of Mecli. Eng., October, 1888, also see 
Hellers “Stresses in Structures,” Art. 13. 



Art. 5. 


A GOOD RIVETED JOINT. 


9 


5. Requirements for a Good Riveted Joint. From the 
discussion in Art. 4 the following conclusions may be drawn: A 
good riveted joint, 

1 . Should he as compact as possible, in order to render the 
uniform distribution of stress more certain. 

2 . Should not he very large, because the workmanship 
cannot be perfect, and there is the greatest danger of uneven 
distribution of stress in a joint having the largest number of 
rivets. With part of the rivets in a joint defective there may be 
eccentric stresses and overstrain, causing a redistribution of 
stress and probably overstrain in other members. 

3. Should have its rivets arranged symmetrically about the 
center lines of stress. 

4. Should have provision for unavoidable eccentric 
stresses (see Art. 12). 

5. Should have rivets of good material, properly driven, 
under uniform conditions. 

6 . Should have a sufficient number of rivets so that there 
will he no slip if the stresses alternate in direction. 

7. Shoidd not have rivets in direct tension. 

6. Proper Sizes of Rivets. The usual sizes of rivets, 
• which are seldom departed from in structural work are y 2 in., 
% in., % in. and % i n - Rivets larger than % in. in diameter 
can not he driven tight hy hand, and in shops, it is not always 
possible to obtain sufficient power to drive them satisfactorily. 

It is a common rule not to use a rivet diameter smaller 
than the thickness of the thickest plate through which it passes, 
because, although somewhat thicker plates can be punched, it is 
often expensive work on account of the breakage of punches. 
If thicker metal is used it must be drilled, and the result is that 
metal of greater thickness than about % in. is avoided. 

Tables giving the maximum size of rivet which can be 
driven in various sizes of structural shapes, and the location 
of the most desirable rivet center lines or “ gages, ” are found 
in the handbooks published by the various steel companies. 1 

Generally it is best to use the largest size of rivet allowable 
in each piece, unless this would result in a number of sizes in 


*See “Cambria,” pages 52, 53, 54 and 314. 




10 


SPACING OF RIVETS. 


Art. 7 


one member, which would cause extra handling in the shop. 
Usually but one or two different diameters of rivets are used in 
an entire structure. When two different diameters of rivets are 
used in one member, the change should be made in such a manner 
that the two sizes of holes do not both come in any large pieces, 
as this would necessitate extra handling in punching. Although 
a % inch rivet may be driven in a 3 inch leg of an angle, a 3V 2 
inch angle should be used to make an important connection with 
% inch rivets. 

7. Spacing of Rivets. Rivets are spaced according to 
practical rules which are almost universal. It is evident that 
rivet holes might be punched so closely together that the metal 
between them would be injured to such an extent that it would 
be of very little value. On the other hand the rivets might be 
so far apart that the parts joined would not be in close contact 
between rivets, leaving a space for water and dirt to lodge, 
causing rust which would buckle the parts and might develop 
high local stresses. Rivets might also be spaced so near the edge 
of a piece that the metal would tear out. 

By “pitch” of rivets is usually meant the distance center 

to center, parallel to the line 
of stress, whether the rivets 
be in the same or in different 
rows. End distances are par¬ 
allel to the line of stress and 
side distances are perpendic¬ 
ular to it. In Fig. 5. 
p=pitch. e=end distance. 
s=side distance. d=diameter 
of rivet. t=thickness of out¬ 
side plate.. 

The following table gives the usual specified limits for rivet 
spacing, and Fig. 5 explains the terms used. 


min. 

gAdicAo 

—G - — 1 — G 

o o;o g 

iTTTmTT i 

max. p~ 6'or /6t 
Fig. 5. 


a 


T 








Art, 7. 


SPACING OF RIVETS. 


11 



Diameter of 

Rivet in inches 

^ Min. Dist. Cent, 
ft. to Cent. Speci¬ 
fied in inches 

Usual Min. Pitch 

for Single Line 

in inches 

Maximum Pitch 

Specified 

Usual Maximum 

Pitch Used 

tvj End Distance 

Specified in in. 

End Distance 

Usually Used 

in inches 

t\> Side Distance 

^ Specified in in. 

Side Distance 

Usually Used 

in inches 



K 

IK 




1 

IK 

1 

1 or G 






rH 

rH 







X 


‘2'A 

• pH 

CO 

•i-H 

CO 

m 

IK 

IK 

IX 



K 

2K 

2 % 

u 

o 

-VJ 

u 

o 

ik 

IK 

iK 

IK 



A 

2 % 

3 

CO 

T—1 

CO 

T—H 


IK 

IK 

IK 



The minimum pitch in a double line may be less than in a 
single line, so long as the distance center to center of holes in 
any direction is not less than the minimum distance specified. 
It is not the usual practice to use the least allowable pitch unless 
there is a good reason j!or not avoiding it. For the maximum 
pitch 16i requires 4 in. for % in. plates and 5 in. for T \ in. 
plates. It is not good practice to exceed these pitches, but in 
some classes of work 6 in. is used as the maximum pitch for all 
thicknesses of plates. In the best classes of work, no metal is 
used in important parts, less than % in. thick, in which case 
16t=6 in. 

The maximum pitch allowed perpendicular to the line of 
stress is usually about twice that allowed parallel to it, but this 
is rarely used except in cover plates of compression members, in 
which case 40t is sometimes allowed. 

At the ends of compression members, the pitch is usually 
3 in. and should not exceed four times the diameter of the rivet 
for a distance equal to about twice the depth of the member. 
This is to insure a uniform distribution of the stress to the sev¬ 
eral component parts of the member. 

The end distance should never be less than iy 2 times the 
diameter of the rivet, and it is usually specified 2 diameters. 
It should never exceed 8 times the diameter of the rivet. 

In the location of rivets it is important to provide clearance 
for the riveting tool. This has a diameter about % in. greater 
than the diameter of the head of the rivet, so that from the 
center of the rivet to the clearance line, the distance should be 



























12 


KINDS OF JOINTS. 


Art. 8 


at least one-half the diameter of the rivet head plus % in. In 
special cases a riveting tool with one side cut off, requiring a 
clearance but little greater than half the diameter of the rivet 
head, may be used. 

Some shops have multiple punches, which punch a number 
of holes at one operation, and are usually used in connection 
with a spacing table. Certain parts are punched on these 
punches and are not laid out by templet. There are limitations 
to the spacing which the table can make, and these must be 
kept in view in making the shop drawings. 


Single Riveted. 


Double Riveted. 










Fig. 6. 






< 

< 

< 

>< 

l i 

c 

c 



o O' 



rf > ) 

s jjj; ■ r/ rr /-t? V 


7 7 



Lap Joints. 


Fig. 7. 


8. Kinds of Joints. Figures 6 to 11 show different kinds 
of riveted joints in plates, and different arrangements of rivets. 
It is evident that a lap joint is much weaker than a butt joint 
with two splice plates. In a lap joint there is a moment, having 
a lever arm equal to the sum of half the thicknesses of the plates. 


Single Riveted 


Single Riveted. 


I© 

| 

!& 







-©!©-- 





^~sp//ce p/afe 


Fig. 8. 



pp//ce p/gfeo ^ ^ 


Butt Joints 


"O' O' 

Fig. 9. 


If there were no deformation, the resulting unit bending stress 
in the plate would be six times the unit stress due to direct 
stress, but as the joint deforms the center lines of the plates ap¬ 
proach each other, as shown in figures 6 and 7, and the moment is 



















































Art 9. 


DESIGN OF RIVETED CONNECTIONS. 


13 


reduced. * The bending of the plates will increase the tensile 
stress in the rivets, and successive changes of stress, if great 
enough would loosen them. 

Butt joints with two splice plates should be used whenever 
possible. 


Staggered Riveting 



Fig. 10. 


Chain Riveting. 



o-o o;o o o 

H 


6 o o|o o o 



O O O'O o o 

— 

_ 

o o o;o o o 




^ /K r\ 

CT\ 


c= 

' ! 


;f 


' \is 

KJ 

O' O' 


Fig. 

11. 



9. Design of Riveted Connections. Riveted joints in 
structural steel work are always designed upon the supposition 
that the rivets carry the stress according to the assumptions 
given at the beginning of Art. 4. 

According to these assumptions a joint may fail in the fol¬ 
lowing ways: 

1. By tearing the parts in tension through a line of rivet 
holes. 

2. By tearing out the metal between the end of the piece 
and the last rivets. 

3. By shearing the rivets on one cross section. 

4. By shearing the rivets on two cross sections. 

5. By crushing the rivet on one or more of the pieces of 
metal joined. 

Provision against tearing through a line of rivet holes in 
tension members, will be treated in Art. 11. 

The end distances usually specified and which are given in 
Art. 7, provide against tearing out at the ends. 

If there is a tendency to shear off a rivet on one cross sec¬ 
tion, it is said to be in single shear, as in figures 6, 7 and 8. If 
there is a tendency to shear the rivet on two cross sections, it is 
said to be in double shear, as in figures 9, 10 and 11. 

It is evident that if two plates be joined together, one of 
them might be so thin that the rivet would be crushed where it 
bears on the plate, before sufficient stress is developed to shear 























14 


DESIGN OF RIVETED CONNECTIONS. 


Art. 9 


the rivet off. As the safety against crushing depends upon the 
area of pressure or bearing, and this depends upon the thickness 
of the plate, a rivet is said to be in bearing on the plate. 

Rivets are therefore proportioned for single shear, double 
shear or bearing. It is possible to have all of these to consider 
in a single joint. 

In a lap joint the rivets are in single shear or bearing, 
depending on the thickness of the plates. In a butt joint with 
two splice plates, the rivets are in bearing or double shear. The 
bearing may be either on the splice plates or on the main plate. 
The splice plates should always be made thick enough so that 
the bearing will be on the main plate. That is, each splice plate 

should be more than half as thick as the main plate. 

* 

There is no very definite relation, generally recognized, 
between the working stresses in tension, shear, and bearing. The 
working stresses for rivets should depend on experiments. Many 
specifications give a shearing unit equal to about three-fourths 
of the tension unit and a value in bearing double that in 
shearing. 1 

The value of a rivet in single shear is simply the product 
of the area of its cross section, by the working unit stress in 
shear. Thus the area of cross section of a % in. rivet is 0.44 
sq. in. and its value in single shear at a shearing unit of 7,500 
lbs. per sq. in. is 7500X0.44=3300 lbs. The value of a rivet in 
double shear is twice its value in single shear. The value of a 
rivet in bearing is taken as the product of the area in bearing 
by the working unit stress in bearing. The area in bearing is 
assumed to be the diameter of the rivet multiplied by the thick¬ 
ness of the piece against which it bears. Thus the value of a 
y s in. rivet in bearing on a y 2 in. plate at 15,000 lbs. per sq. 
in. is M>X%X 15000=6,562 lbs. In designing riveted joints the 
strength of a rivet is always figured at its diameter before driv¬ 
ing. Tables of values of rivets in shear and bearing for several 
different working stresses, are given in “Cambria,” pages 
310 and 311. 

On account of the inferiority of field driven rivets an excess 
of from 25% to 50% over the requirements for power driven 

1 For experiments on the ultimate resistance of steel and iron 
plate s in bearing see Johnson’s “ Materials of Construction,'' 1 Cliapt. XXVI. 




Art. 10. 


EXAMPLES OF RIVETED JOINTS. 


15 


rivets is usually specified. The frictional resistance is much 
less with hand driven than with power driven rivets. 

The value allowed for rivets with countersunk heads varies 
with different specifications. If the metal, in which the counter¬ 
sinking is done, is thick enough to give sufficient bearing below 
the countersunken part to develop single shear in the rivet, no 
reduction need be made from the value used for rivets with full 
heads. Xo reduction is usually made when the heads are only 
flattened. Rivet heads inch or less high are countersunk. 

10. Examples of Riveted Joints. A few examples of the 
usual forms of riveted joints will now be taken up. In all of the 
examples in the remainder of this chapter we will assume the. 
following data: 

Allowed shearing on rivets 7,500 lbs. per sq. in. 

Allowed bearing on rivets 15,000 lbs. per sq. in. 

All rivets % in. in diameter. 

The values of rivets in single shear, double shear, and bear¬ 
ing, may be taken from “Cambria,” pages 310 and 311. 

Figure 6. The rivets in this single lap joint will transmit 
3X4510=13,530 lbs. in single shear, but if either of the plates 
be less than % in. thick thq value of the rivets in bearing on the 
plate will be less than the single shear value, and the amounc 
of stress which the joint will transmit, will be less than 13,500 
lbs. If the plates are in. thick, the rivets will transmit 
only 3X4102=12,306 lbs. 

The zigzag line in the table in “Cambria,” as explained at 
the bottom of the page, separates those bearing values which are 
less from those which are greater than single shear values. 

Figure 10. In this butt joint with two splice plates it is 
evident that the stress must go from the main plate on one side 
of the splice, to the rivets on that side, from these to the splice 
plates, from the splice plates to the rivets on the other side, and 
through them to the other main plate. 

The rivets are in double shear if the plates are thick enough. 
From “Cambria” we find that the value of a % in. rivet in 
bearing on a in. plate is equal to its value in double shear. 
If therefore the main plate is \ J in. thick or thicker, and the 
thickness of each splice plate is sufficient to develop single shear 
in the rivets (% in. or more), the rivets of the joint will transmit 



16 


EXAMPLES OF RIVETED JOINTS. 


Art. 10 


7X9020=63,140 lbs. If the splice plates are only y 5 6 in. thick, 
for example, the rivets will transmit only 14X4102=57,428 lbs. 
As stated in Art. 9, the sum of the thicknesses of the splice 
plates should always be greater than the thickness of the main 
plate. 

Figure 12 shows the lower end of a post which resists, 
through the pin, the vertical component of the stress in the 
diagonal tension member. The post consists of two channels 
12 in. x 25 lbs. The pin bears against the post in an upward 
direction, and it is necessary to reinforce the webs of the chan¬ 



nels in order that the pin shall not crush them. Pins are figured 
in shearing, and bearing, exactly similar to rivets, and usually 
the same unit stresses are used. .Pins must also be figured in 
bending, and this will be treated in Chapter VII. 

Assuming the total stress on the post to be 175,000 lbs., 
the stress in each channel will be 87,500 lbs. The thickness of 
bearing on the pin, required to take this stress will be 

87500 — =1.30 in. The total thickness of pin plates required 
4 y 2 X 15000 

is 1.30 in. minus the thickness of the channel web, which is 
0.39 in. (See “Cambria,” p. 164.) The pin plates must then be 



















































Art. 10. 


EXAMPLES OF RIVETED JOINTS. 


17 


1.30—0.39=0.91 in. thick or say jf in., and may be made up of 
one in. and one % in. plate as shown. 

Enough rivets must be put through the pin plates to carry 
the stresses which they get from the pin to the web of the chan¬ 
nel. The total stress 87,500 lbs. from the pin, is distributed over 
H inches thickness of bearing as follows: 

% in. channel web carries /r X 87500=25,000 lbs. 

% in. pin plate carries T 6 r X87500=25,000 lbs. 

T 9 g- in. pin plate carries y 9 T X 87500=37,500 lbs. 

Total=87,500 lbs. 

There must be enough rivets through each pin plate to 
transmit its proportion of the stress to the channel web, and 
there must be enough rivets through the channel web to transmit 
to it all of the stress from both pin plates. 

For that portion of the web which has a pin plate on each 
side, the rivets will be in bearing on the web, if the web is not 
thick enough to develop double shear in the rivets, and each 
rivet will transmit from each pin plate, one half the value of a 
rivet in bearing on the web. Therefore the number of rivets 
required through the thinner pin plate, will be found by divid¬ 
ing the stress carried by this plate, by one half the bearing value 
of a rivet on the web. 

25000 

— =11 rivets required through the % in. pin plate. 

3^ X 4920 ^ * 

These 11 rivets will transmit the same amount of stress to 
the web, from the thicker plate on the other side of the web as 
from the thinner plate. In addition to these 11 rivets, there 
will be required through the thicker plate sufficient rivets to 
transfer the difference between the stresses in the two pin plates, 
to the web by single shear on the rivets. 

37500—25000=12500 lbs. - 125Q P — =3 rivets required 

4510 

through the in. pin plate, in addition to the 11 rivets through 
both. 

It is better to have the pin plates on opposite sides of the 
web as shown, but if necessary, both plates may be put on the 
same side, in which case the number of rivets required through 







18 


EXAMPLES OF RIVETED JOINTS. 


Art. 10 


each would be determined by single shear, and these numbers 
would have to be added together to determine the total number 
required through the web, as none of the rivet values would be 
determined by bearing on the web, unless the web were not 
thick enough to develop single shear in the rivets. 

In this example, the rivets below the pin have been counted, 
but it is evident that they can get no stress except by tension 
in the pin plates. No more stress can be transmitted to these 
rivets than can be carried by the net area of the pin plates at 
the sides of the pin hole. 

Also usually, some of the rivets at a joint like this, have to 
be countersunk on account of clearances, in which case their 
values must be reduced according to the specifications used as 
stated in Art. 9. 




Figure 13 shows the top chord of a bridge at the hip joint. 
The chord section is made up as follows: 





























































Art, 10. 


EXAMPLES OF RIVETED JOINTS. 


19 


1 cover plate, 22 in. X % in- 

2 web plates, 20 in. X re in. 

2 top angles, 3 y 2 in. X 3 y 2 in. X % in. 

2 bottom angles, 4 in. X 31/2 in. X % in. 

We will assume a stress in this chord section of 420,000 lbs., 
and that the pin is 6% in. in diameter. This then will require 

a bearing on the pin of =4.4 inches, or say 2V 4 inches 

on each side. This bearing thickness may be made np as follows: 


Web plate . in. 

Inside pin plate . % in. 

Outside pin plate . % in. 

Outside pin plate . in. 


Total—2% in.= ff in. 

The stress will be distributed over the plates as follows: 

x 9 6 in. Web plate, & X 210,000=52,500 lbs. 

% in. inside pin plate, ^X210,000=58,300 lbs. 

% in. outside pin plate J-j-X210,000=58,300 lbs. 

T V in. outside pin plate X210,000=40,900 lbs. 

Total=210,000 lbs. 

The rivets in that portion of the web, covered by pin plates 
on both sides, will be in bearing on the web. The web not being 
thick enough to develop double shear in the rivets. The bearing 
value of a rivet on the in. web is 7,383 lbs. The number 
of rivets required in the T V in. outside, pin plate will be 

—- 10900 - =11 rivets. The number required in the % in. inside 
X X 7383 

pin plate will be =16 rivets. More rivets than required 

are used in each of these plates, to insure a distribution of 
stress to the upper and lower rivets, and to give such an ar¬ 
rangement as will put the center of gravity of all the rivets as 
near as possible to the center line of stress. 

The number of rivets through the outside pin plate between 
the angles, is determined by the single shear value of a rivet and 













20 


EXAMPLES OF RIVETED JOINTS. 


Art. 10 


is equal to ——13 rivets, all of which must be placed beyond 

the rivets required by the other two pin plates. As there is an 
excess of three rivets in the two other pin plates, one of the 
rivets enclosed by the dotted line at “a” may be counted for 
the outside % in. pin plate. 

Strictly, the rivets passing through the top and bottom 
angles are in double shear, instead of bearing, because the angles 
and web are both a part of the main chord section, and are held 
together by rivets beyond the pin plates. These together make 
up a thickness more than great enough to develop double shear 
in the rivets. A filler 1/4 in. thick will be required in this case, 
under the r V in. outside pin plate, on the top angle. This 
filler, of course, takes no stress. 

One outside pin plate, and all inside pin plates, should take 
rivets through the angles, in order that the stress may be dis¬ 
tributed over he entire chord section, and to the top plate in 
particular. 

This even distribution of the stress requires that the rivets 
in the ends of compression members, for a distance equal to 
about twice the depth, should be spaced closely together, as 
stated in Art. 7. 

No pin plate should be shorter than its width, approxi¬ 
mately, or it might not be strong enough to carry the stress from 
the pin to the outer rows of rivets. One of the pin plates should 
be long enough to extend at least six inches beyond the end of 
the batten plate. 

Here, as in Fig. 12, some of the rivets usually have to be 
countersunk and their values must be reduced accordingly. 

11. Net Sections of Tension Members. In a tension 
member it is not only necessary to have, in a connection or splice, 
a sufficient number of rivets, but there must also be a sufficient 
net area in the parts joined, and in the pieces joining them, to 
safely carry the stress. Therefore in tension members of a 
structure with riveted connections, there must be an excess of 
material, because the joints at their ends, and any splices in 
them, cannot be made as strong as the body of the member. 

Fig. 14 shows a simple tension splice, so made that the net 
area is as great as possible, and the waste therefore, as small as 



Art, 11. 


NET SECTIONS OF TENSION MEMBERS. * 


21 


possible. If the stress to be transmitted across the joint is 65,000 

lbs., it will require =10 rivets in bearing on the y 2 inch 

plate on each side of the splice. 

For getting net areas, the size of the rivet hole is always 
taken as % in. larger than the rivet, or 1 in. in diameter for a 
% in. rivet. At the section AB, the net width of the main plate 
is 11 in. The net area therefore is 11X 1 /^—5.5 sq. in. If the 
allowed unit stress in tension is 12,000 lbs. per sq. in., this net 
area will transmit 5.5X12,000=66,000 lbs. Therefore there is 
sufficient net area at AB. 



Fig. 14. 


At the section CD the net area is lOX^—^.O sq. in., which 
at 12,000 lbs. per sq. in. is good for 60,000 lbs. The rivet at T 
has reduced the stress carried by the main V 2 in. plate at CD 
to 65,000—6,560=58,440 lbs. There is then a little more net 
area on the line CD than is necessary to carry the stress. 

The stress carried by the main y 2 in. plate at EF is 
65,000—3X6,560=45,320 lbs. The net section is 9 XV 2 = 4.5 sq. 
in., which is good for 54,000 lbs. In like manner the stress in 
the main plate at GTI is 65,000—6X6,560=25,640 lbs., while 
the net section at GII is able to carry 8 XV 2 X 12,000=48,000 lbs. 

The net area of the splice plates at any section must also 
be sufficient to carry the stress in them, without exceeding the 
allowed tension unit. At GII the stress in the two splice plates 

is 65,000 lbs. This will require a net area °f “ 1 ^ 55 = 5.42 sq. in. 
The net width of the plates at the point is 12—4=8 in., which 





















22 


NET SECTIONS OF TENSION MEMBERS. 


Art. 11 


5 42 

will give a required thickness of the two splice plates of —=.68 

in. and hence each plate will have to be % in. thick. 

The stress carried by the splice plates at EF is 65,000—4X 

0017(50 

6,560=38,760 lbs. The required net area is - =3.23 sq. in., 

3 23 

which will require a net width of 0 ' . .. =4.31 in., or a gross 

" X 78 

width of 4,31-f-3=7.31 in. The width of the splice plates may 
be reduced here some, but not in this case to the limit of 7.31 in. 
because this would not give sufficient edge distance beyond riv¬ 
ets K and L. 

In figuring these net areas, only square sections have been 
taken. It is obvious that if the lines of rivets GH and EF for 
instance, are close enough together, the zigzag section 
GKMPNLII will have less net area than the square section GH. 
Experiments have been made on steel plates which seem to in¬ 
dicate that rupture will take place on the zigzag line unless its 
area exceeds the area on the square section by at least 30%, 1 
and some specificaions require net sections to be figured on this 
basis. Other experiments seem to show that rupture is equally 
probable on square or zigzag sections if the net areas are equal. 2 
None of these experiments may be a good guide, because there 
is no doubt an entirely different distribution of stress after the 
elastic limit is exceeded than before, on account of the unequal 
deformation and distortion produced. 

This is a difficult matter to investigate theoretically, and 
until further experiments are made, it is well to be liberal in 
allowances for rivet holes. In Fig. 14 the distance between the 
rivet lines GH and EF which would be necessary to give 30% 
excess to the zig zag line GKLII over the square section GH, is 
nearly 3 in., and if the transverse spacing were greater, this 
longitudinal distance would also have to be larger. 

In nearly all cases in practice, the least area is taken, 
whether it he zigzag or square section, and no attention is paid 
to the 30% rule, unless specially required by the specifications. 
Some specifications give a simple rule like the following: 

^ee articles by Prof. A. B. W. Kennedy in Trans. Inst. Mech. Eng , 
1881, 1882, 1885 and 1888. 

2 See Engineering News, May 3. 1906, Vol. LV, page 488. 




Art. 11. 


NET SECTIONS OF TENSION MEMBERS. 


23 


“The number of rivet holes to be allowed for in getting net 
section shall be the greatest number whose centers are 1% in. 1 
or less from any possible square cross section.” According to 
this rule the rows of rivets would have to be more than 2% in. 
apart, if the holes in but one row were to be deducted. This rule 
is not a safe one to follow in all cases, as will be seen later. 

A common case is that of an angle, which may be considered 
like a plate developed, as in Figs. 15, 16 and 17. The width of 
the plate will be equal to the sum of the legs of the angle less its 
thickness. There are four cases according as the angle has one, 
two, three, or four lines of rivets. 

In getting the net area of an angle with one line of rivets, 
allowance is made for the area cut out by one hole; with two 

lines for one or two 
holes; with three 
lines for one, two, or 
three holes, and with 
four lines, for one, 
two, three or four 
holes, depending 
upon the pitch. 

In Fig. 15 the 
stagger of the holes in the two legs is 1% in., and according to 
the practical rule above, the net section is equal to the gross 
section, less the area cut out by two holes, or 2.75—2X%—1-75 
sq. in. It is evident that the holes cut out a large percentage 
of the material. The square section on AE has an area of 
2.75—1X%=2.25 sq. in., while the zigzag area ABCD is 
(3.47 — 1+2X%) X%—1-98 sq. in., showing a deficiency in 
place of an excess in the zigzag area. 

By working the problem in the other direction we can easily 
find the stagger of holes necessary to give us either an equal area 
or a 30% excess on the zigzag line, over the square section. In 
the case of Fig. 15. it would require the stagger to be at least 
4 y 7 g in. in order that only one hole need be deducted according 
to the 30% rule. This would make the holes in one line at least 
8 % in* apart. 

The following table gives the necessary stagger of rivets in 
Various specifications give the distance from 1 % in. to 2% in. 




















24 


NET SECTIONS OF TENSION MEMBERS. 


Art. 11 


several sizes of angles with one line of rivets in each leg, to give 
an equal area and 30% excess area on the zigzag section, com¬ 
pared with a square cross section through one hole. By this 
table we see that the areas given by the practical rule are not 
always safe. 


Size of Angles in Inches 

CO 

V 

Xt 

* 8 

V —* 

U - 

Size of Rivet 

in inches 

Area through 

1 hole 

Stagger for 

equal area 

in inches 

Area plus 

10% 

Stagger for 

30% excess 

area in ii. 

2X2X J 4 . 

1 X 

H 

0.75 

1.89 

0.98 

3.04 

!>i,; X •,•>£ < M •. 

1% 

% 

0.97 

2.26 

1 26 

3.78 

3X3XK . 



1.73 

2.69 

2.25 

5.53 

3^X3 HXH . 

2 

Fs 

2.75 

2 83 

3.57 

5.05 

•1 X 1 X H . 


% 

3.25 

3.00 

422 

5.68 



would doubtless take place on EFCD or ABCD but according to 
the 30% rule three holes would have to be deducted. 


In Fig. 17 the area on AF is 5.75— 1XV2=^.25 sq. in. The 
area on ACG is %>(4.-f-6.19-|-1.5—2)=4.84 sq. in. The area on 
ACDE is 1 / 2 (1-5—f—3.9—(—6.19—f—1.5—3)=5.04 sq. in. The area on 
ABODE is i/ 2 (1.5+3.9+3.81+3.9+1.5-4)=5.31 sq. in. The 
weakest section is ACG apparently, and failure would probably 
take place on this section, even though the sections ABODE and 
ACDE have far less than 30% excess area over any square 
section. 

If the 30% rule were followed it would be necessary to make 
































































Art. 11. 


NET SECTIONS OF TENSION MEMBERS. 


25 


allowance for two holes at least, in any angle having holes in 
both legs, if the maximum allowed pitch were not exceeded. (7) 
In order to provide against undiscovered defects in work¬ 
manship and material, it is well to make a liberal allowance in 
calculating net areas, especially where stresses are eccentric, as 
they usually are in angles. 1 

Practice is not at all uniform on this point. 



12. Eccentric Stresses in Riveted Connections. Eccen¬ 
tric stresses are seldom calculated. They should always be 
avoided if possible. 

It is evident that a single lap joint like Fig. 6 is eccentric. 
The forces form a couple with a lever arm equal to half the sum 
of the thicknesses of the plates joined, tending to bend the plates 
and the rivets (Art. 8). The plates are therefore subjected to a 
bending and a direct stress. In a butt joint with two splice 
plates,’ (Fig. 9), there are no eccentric stresses in the plates 
joined, but there are in the splice plates. 

Figure 18 shows a common form of eccentric connection. 
The eccentricity might be avoided by moving the force P to P' 
so that its line of action will pass through the center of gravity 

hBee Engineering News, Vol. LVI, page 14 (July 5, 1906) for an 
account of experiments 'by Prof. Frank P. McKibben, which show that 
the eccentricity of stress in angles causes rupture to occur at about 
80% of the ultimate strength of test pieces cut from the same material. 






































26 


ECCENTRIC RIVETED CONNECTIONS. 


Art. 12 


of the group of resisting rivets. If it is impossible to avoid the 
eccentricity, the stresses on the rivets may be found as follows. 

The force P, of 16,000 lbs., may be replaced by an equal 
force P' parallel to it, and a couple whose moment is 16000X 
3.18=50,800 in. lbs. 1 



To resist rotation about the center of gravity of the group 
of resisting rivets, each rivet acts in a direction perpendicular 
to its lever arm and thus takes an additional stress in proportion 
to its distance from the center of gravity of the group. If S' 
be the stress on each outermost rivet, due to the moment, the 

equation of moments will be 2X4.5S'-|-2Xl 1 /2y^ : |- S'=50,800 

in. lbs., from which we get S'=5080 lbs. 

The maximum stress on each outer rivet will be the result¬ 
ant of 4000 lbs. and 5080 lbs., which may be obtained graphically 
as shown in Fig. 18. The resultant for the two outer rivets will 
not be the same, because the stresses due to the tendency to 
rotate act in opposite directions. If the greater of these result¬ 
ants exceeds the allowed stress on one rivet, more rivets must be 
used. The resultant for rivet A is 8,370 lbs., and is the greater 
as would naturally be expected. It is more than double the 
stress (4000 lbs.) that it would receive if there were no eccen¬ 
tricity. 

^his is an abstract proposition. See Rankine’s “ Applied Mechan¬ 
ics," Art. 42, also Heller’s “Stresses in Structures Art. 34. 


















Art. 12. 


ECCENTRIC RIVETED CONNECTIONS. 


27 


Figure 19 shows another common form of eccentric connec¬ 
tion. The direct stress on each rivet is =2,500 lbs. The 
total moment is 20,000X1-42=148,400 in. lbs. Writing the 
equation of moments we have 4X7*5S'+4X6.17y^- , S / =148,400 

in. lbs. Solving, we get S'=2,950 lbs., which is the stress on A, 
B , C, or I) due to the moment. These stresses act in the direc¬ 
tions shown in the figure, which also shows the direct stress on 
each rivet. Finding graphically, the resultants of the two forces 
which act on each outer rivet we have for A 630 lbs., for B 
3600 lbs., for C 5,410 lbs., for D 4,080 lbs. The stress on C is 
more than double what it would be if P were applied in the 
line of P'. 




It is seen from these examples, that if the connection is 
eccentric, the rivets are not equally stressed, and that simply 
taking into account the direct stress will often give results far 
from the truth. 

In laying out a joint in which several members connect, 
rivet lines are often taken in place of center of gravity lines. 
This is permissable only when the resulting eccentric stresses 
come within proper limits. If the rivets in a joint are not sym¬ 
metrically arranged about the neutral axes of the members, 













28 


SHOWING RIVETS ON DRAWINGS. 


Art. 13 


there will be eccentric stresses. An angle connected by one or 
both legs forms an eccentric connection which cannot be avoided. 
(See foot note, page 25.) 

13. Showing Rivets on Drawings. In general only rivet 
heads in plan are shown on drawings. They should always he 
drawn to scale. 'Where there is any possibility of interference 
the rivet heads may be shown in elevation as well as in plan. In 
such cases the heads are sometimes only drawn in pencil to de¬ 
termine the clearance. 

In certain locations there is not room enough for a full head, 
therefore rivet heads may be flattened or countersunk as shown 
in Fig. 20. By this means heads may be made flush with the 
metal through which they are driven, or be made % in., in. 
or % in. high. The usual symbols indicating these various kinds 
of heads are shown in Fig. 20, which also shows how open holes 
(into which rivets are to be driven in the field) are indicated. 
This is called the Osborn system of symbols, and is practically 
universal in this country now. 



F/e/c/ RiveAs 


<- 

P/a/n 

Countersunk ana/ . 

Countersunk not . 

ftaffenect 

---> 

... fattened 

ft 


c 

^ 

£~h/qh 

$ 

S'! 

# h/ah vj 

^ ^ ^ 

i 


7* 

/ih fa, 

(•) <S) -- 





m w w! 

^ w 

(f) w 

w 

w * wl 


Fig. 20. 


All the rivets in a member need not be shown on a drawing, 
but all of the rivets at the joints should be drawn in. The inter¬ 
mediate portions of the members are frequently omitted and the 
spacing indicated as so many spaces at so much. In this case the 
spacing so given should tie up two definitely fixed points at the 
ends. 














































CHAPTER II. 

DESIGNING AND ESTIMATING. 


14. Classes of Structural Steel Work. Ordinarily the 
term “structural steel” covers only the rolled steel used in 
structures, and does not include any castings or machinery; but 
in many classes of work, machinery is so intimately connected 
with the structure as to render the separate design of the two 
impossible. 

The field of usefulness of steel in structural work is being 
constantly extended, and the problems of its design becoming 

more complex, especially for work in the more populus districts 

» 

of the country. 

The following is a list of the more important kinds of struc¬ 
tural steel work: 

Bridges for steam and electric railways and highways, 
I-Beam spans, 

Longitudinal trough floor spans, 

Through and deck plate girder spans, 

Combination bridges (wood and steel), 

Simple truss spans, 

Draw-bridges (swing, lift, rolling, bascule, etc.), 
Viaducts or trestles, 

Elevated railways, 

Arch bridges, 

Suspension bridges, 

Turntables for locomotives, 

Trainsheds, 

Steel mill and factory buildings, 

Steel roof trusses, 

Grandstands, 

Steel work for tall office buildings, 

Stand pipes and elevated tanks and towers, 

Steel canal lock gates, 

Traveling crane girders, 

Ore conveyor bridges, 

Car unloaders, 

Bins for ore, coal, coke, grain, etc. 


29 


30 


KINDS OF SHOPS. 


Art. 15 


15. Kinds of Shops. It may be said that no single plant 
in this country is well equipped for turning out all of the differ¬ 
ent kinds of structures enumerated in the preceding article. 
Some are confined to the manufacture of railway bridges, heavy 
highway bridges, and heavy building work, some to highway 
bridges and light building work, some to steel work for build¬ 
ings, some shops are not equipped to make pin connected work 
and others cannot do girder work economically. Some shops are 
not fitted to handle reamed work. (2). 

These facts are sometimes emphasized by the manufacturer 
in order that he may be allowed to make his own designs, but 
this should not be given too much weight by the purchaser, as 
all the usual forms of details can be executed in any shop fitted 
for the particular kind of work under consideration and there 
will seldom be any difference in price to the purchaser, unless 
the form of detail is an unusual one. 

16. Proposals and Contracts. The requirements of var¬ 
ious purchasers in regard to proposals and contracts are not at 
all uniform. The law requires that public officials advertise for 
proposals on public work, and any manufacturer who meets the 
requirements must be allowed to bid. The laws differ in the 
various states. Private corporations, companies and individuals 
do not usually advertise for bids, but invite proposals from such 
manufacturers as they desire to compete for the work. They 
very seldom require the deposit of a certified check with the pro¬ 
posal to insure the signing of a contract by the successful 
bidder, or the furnishing of a bond to insure the fulfillment of 
the contract. The certified check and bond are usually required 
on public work. 

If the purchaser does not furnish a design or plans of the 
work, each manufacturer submits his own design with his pro¬ 
posal. This may be in accordance with specifications of his own 
or with some standard specifications. The letting of the contract 
then becomes a question not only of the lowest bid but also of 
the most desirable design. Usually the manufacturer submits 
only a stress and section sheet, commonly called a strain sheet, 
but sometimes “show” plans, showing the general appearance 
of the structure and some details of construction are also sub¬ 
mitted with the strain sheet. Show plans are frequently nothing 


Art. 17. 


DESIGNS AND ESTIMATES. 


31 


more than ornamental drawings on which the lettering and 
shade lines play an important part. 

Railroads have bridge engineering departments which pre¬ 
pare the plans for the bridges. These, together with standard 
specifications, are submitted to the bidders who then all bid 
upon the same thing. 

17. Designs and Estimates. When an improvement is 
contemplated the purchaser should employ some one who is 
competent to prepare plans and specifications and estimates of 
cost of the proposed work. Also, before making a proposal, the 
manufacturer must make an estimate of cost, and if no plans 
are submitted by the purchaser on which to base the proposal, 
he must also prepare a design and plans to accompany his bid. 
In either case the method of procedure in making the designs 
and estimates will be essentially the same. In the case of the 
manufacturer this work is done by the estimating department. 

Designs and estimates must frecpiently be prepared upon 
the shortest notice, and in any case must be cornpleted before 
the time set for receiving bids. Certain methods of doing the 
work of the estimating deparment are of the highest importance, 
as they save time and reduce the liability of errors. 

Proposals for bridge work are asked for either “lump sum” 
or per pound. In case a lump sum price is required a very care¬ 
ful estimate is necessary. Usually when a pound price is given, 
only an approximate estimate is made to give a general idea of 
the various quantities of materials involved. 

The estimate of cost includes such items as The following: 


Material, 

Steel from the mill (various shapes take different prices). 


Eye-bars, 

Castings, 

Buckle plates, 
Hand railing, etc.. 


In case these are not manufactured 
by the bidder in question. 


Labor of manufacture, 
Shop labor, 

Drafting, 

General expense, 
Freight, Haul, 




32 


DESIGNS AND ESTIMATES. 


Art. 17 


Erection (staging and false work) Painting, 

Lumber, 

Sub-contract work as paving, masonry work, etc. 

Before the cost estimate can be made, of course the various 

« 

quantities of material required must be determined. 

The data furnished for making the design, are frequently 
very meager but usually include specifications, profiles and maps 
of the location. 

Before starting on a design and estimate, the first thing 
the designer has to do is to familiarize himself with the require¬ 
ments and conditions to be met. Of these requirements the 
specification is often the only one of importance, although in 
some cases other matters may demand more study. The specifi¬ 
cation is a guide giving the kind of material to use, the loads to 
be assumed as acting on the structure, the unit stresses allowed, 
the kinds of details desired, the quality of the workmanship, etc. 
These will be discussed more fully in Art. 20. 

If the design is to go in competition with others it is im¬ 
portant that it be an economical one, that is, the weight must 
generally be as small as possible and still meet the requirements 
of the specifications. This is of course important to the purchaser 
in any case. Designing of structures is not such an exact science 
that it may be said that all material in excess of what is required 
to take the calculated stresses is wasted, but the lightest struc¬ 
ture is generally the cheapest and usually the price is the most 
important determining factor in selecting a design. Each case 
must, however, be treated according to the peculiar conditions 
surrounding it. Only engineers of experience can design really 
economic structures. This matter is an important one because 
it is a matter of producing a structure to perform a certain 
function safely and at a minimum cost, j 

No two estimating departments use exactly the same meth¬ 
ods. The following will give the essential points. 

In order that the important requirements of the specifica¬ 
tion may be easily found they may be underscored on the first 
reading, or an abstract made omitting such parts as are common 
to all specifications and such parts as do not affect the design. 
If a blank form is used for this abstract it will be better for 
reference. Calculations should be kept in some permanent form 


Art. 17. 


DESIGNS AND ESTIMATES. 


33 


for future reference, the name of the structure and the date 
being prominently indicated. 


Span Extreme ._ 

Roadway- - _ 

Span C. to C.__ 

Panels at_ 

Estimated > f Steel 

DL per ft. j j Floor & Track . 

Total Steel _ 

Steel per ft._ 

Total Lumber_ 

Sidewalk _ _ 

Capacity Trusses 

Capacity Floor _ 

Specifications 

Depth C. to C. —_ 

Length of Diag. __ 

Sec. Tg. 

Total 

Panel Load per Truss DL _ 

« .LL _ __ 


*ORM No. t 


THE OHIO STATE BRIDGE COMPANY 


Sheet No_ 

Estimate for_ 


Made by. 


Date. 


( TTi/'s space for Diagram.) 


MEM 

DL 

Sires* 

LL 

Stress 

Impact 

Total 

Stress 

Unit 

Stress 

Req. 

Area 

MATERIAL 

Actual 

Area 

No. 

Pcs. 

Wt. 
P. FI. 

Length 

WEIGHT 





















































* 












































Form No. 1. The Form shown in Fig. 22 is to be used in connection 
with this one. 

Fig. 21. 


# FORM NO. 2 

THE OHIO STAtE BRIDGE COMPANY 

Sheet No-- Made by__ _ Date______ 

Estimate for ____ __ _ _ __ _ _ 

MEM 

DL 

Stress 

LL 

Stress 

Impact 

Total 

Stress 

Unit 

Stress 

Req. 

Area 

MATERIAL 

Actual 

Area 

No. 

Pcs. 

wt. 
P. Ft. 

Length 

WEIGHT 


















- 





















































































































Form No. 2. This Form is used in connection with Form No. 1. 

Fig. 22. 






































































































34 


DESIGNS AND ESTIMATES. 


Art. 17 


The information used in making* estimates of weight and 
cost, and stress and section sheets, is set down on blank forms 
called estimate sheets. If the estimate is from plans giving 
more or less detail, a form like Fig. 23, may be used. If a design 
is made in connection with the estimate, blanks like Figs. 21 
and 22 are used. The usual size of these is 814x14 inches. 

■ ■ • ■' - ■ ---■ ■■ ■ ■■ ■ ■ ■ ■ 1 ■ 1 '» ~ 

FORM No. 3 

.THE OHIO STATE BRIDGE COMPANY 

Sheet No.__ Made by_ Date_ 

Estimate for________ 


MEM. 

No. 

SIZE 

length 

wt. 

P. Ft. 

WEIfiUIS 












TOTAL 

























- 














































































































































































































































SS 


































Form No. 3. 
Fig. 23. 


On Form No. 1, in the space at the top, should be shown a 
single line diagram of the structure, properly lettered. (For 
example see Art. 62.) This form also has places for the prin¬ 
cipal data upon which the design is based, stresses, make up and 
areas of members and their estimated weights. This form is used 
for sheet No. 1 of the estimate. For the following sheets Form 
No. 2 is used, which is similar to the lower part of Form No. 1. 

An estimate should give within a few percent, the actual 
quantities of the various materials, which will be required to 
make the structure. An estimator must, therefore, not only 
know how to obtain the weights of main members, but he must 
be thoroughly familiar with detailing. 

Unless the estimate is made from plans giving details, or is 
for a plate girder bridge, or some such simple structure, the 
details are not all set down, but are lumped as a percentage of 
the main parts. A convenient way of doing this, for pin con¬ 
nected trusses, is to make the details of each member, a per¬ 
centage of the rest of the member, and for riveted trusses, a 






























































Art, 18. 


TIME SAYERS. 


35 


percentage of the balance of the whole truss. Of course these 
percentages will vary with the specifications and form of truss, 
and must be determined by making an estimate of the details, or 
by taking them from previous estimates in which the details 
have been estimated. 

An estimating department accumulates, in time, many 
valuable tables, such as tables of standard connections, joists, 
rivet and pin values, portal stresses, properties of columns, 
moment tables, etc., which save much time. Much valuable in¬ 
formation is given in the handbooks published by mills rolling 
structural steel shapes. Those gotten out by the Carnegie Steel 
Co. and the Cambria Steel Co. are the most complete. Since 
• they give the properties of all rolled shapes, one of them is in¬ 
dispensable in making designs and estimates. Combinations of 
shapes are frequently used for compression members and girders. 
Since it is necessary to know the radius of gyration or moment 
of inertia of these and the location of the neutral axes, and 
since calculating these involves considerable labor, there should 
be some systematic method of making the calculations and of 
preserving the results for future reference. There are several 
sets of tables published, giving the properties of builtup sections, 
and one of these will be a great help in designing. 1 

18. Time Savers. Besides the books and tables above 
referred to there are several instruments, the use of which will 
save much time and mental effort and reduce mistakes to a 
minimum. 

The most important of these is the slide ride. It is, in fact, 
indispensable in this sort of work. Thacker’s cylindrical slide 
ride or the Fuller rule are more accurate than is necessary for 
the ordinary work of the estimating department. A rule which 
will give results with a maximum error of one in two hundred 
is sufficiently accurate for all ordinary purposes. The Thacher 
rule is, of course, very convenient when more refined work is 
desired. It will give results with a maximum error of about 
one in ten thousand. 

The ordinary ten inch Manheim rule will answer very well, 
but one which will give the product of three numbers at one 

Osborn's Tables” by Frank C. Osborn. 

“Properties of Steel Sections” by John C. Sample. 



36 


TIME SAYERS. 


Art. 18 


setting is very convenient. In getting weights, the number of 
pieces, the weight per foot and the length are multiplied to¬ 
gether. There are several rules on which this operation can be 
performed at one setting. The “Duplex” rule is one. This rule 
is ten inches long and the setting is made on one face and the 
result read on the other by means of a runner. On the “Engi¬ 
neer’s Slide Rule” the entire operation is performed on one face 
at one setting. This rule is twenty-four inches long and has no 
runner. The great advantage of this rule, aside from its three 
multiple feature, is the ease with which it may be read. There 
are only'a few more divisions in the twenty-four inches than 
are given on the other rules in ten inches, and consequently the 
continued use of the rule is not nearly so trying on the eyes. 
The degree of accuracy is not much greater than that of the ten 
inch rules. The maximum error of operations on the three 
multiple face is about one in two hundred. On the other face 
of the rule is an ordinary slide rule with scales twenty-four 
inches long, which gives results within one in five hundred with 
the same ease on the eyes. 

Care should be taken to select a rule which works easily but 
not loosely, and one in which the graduations on the slide cor¬ 
respond with those on the rule. The trial of a few simple num¬ 
bers will be a sufficient test of its accuracy. For instance, when 
the 1 and 2 are set opposite the following multiples should also 
read exactly opposite: 2 to 4, 2.5 to 5, 3 to 6, etc. A rule with 
a white celluloid face is preferable. 

The scales on the slide rule being logarithmic, problems 
involving multiplication, division, powers and roots can be solved 
by its use. The books of instruction, which accompany the rules, 
explain their use fully, but the method of operation can easily 
be discovered by trial with simple problems. Some definite 
method of operation should be adopted and always followed, to 
save time, so that it will be unnecessary to reason out the process 
each time a multiplication is performed. Most problems may be 

resolved into the simple form of and for these the 

following simple rwk is convenient: “Keep the DIVISOR on 
the SLIDE and read the ANSWER on the OUTSIDE.” Of 
course, any one of the three factors may be unity, which pro¬ 
vides for simple multiplication and division. 



Art. 19. 


ORDER OF ESTIMATING. 


37 


The decimal point is best located by inspection after the 
result has been set down. 

If many estimates are made in one office, it should be pro¬ 
vided with some kind of an adding machine. There are several 
such machines manufactured in this and other countries. An 
elaborate machine, such as is used in banks and clearing houses, 
is not necessary. The * * Computometer ’ ’ is an excellent machine 
but is somewhat expensive. A small instrument like the “ Rapid 
Computer” is not so expensive and will answer very well. 

19. Order of Estimating. It is, of course, very important 
that all multiplications and additions be correct within certain 
limits, and every check possible should be employed. It is also 
very important that no omissions are made. The best way to 
insure reliable results and at the same time secure speed in esti¬ 
mating, is to follow some fixed order of performing the work 
and some definite form of setting it down. 

The following forms have been used by the author and 
will serve as illustrations: 




* 


38 


ORDER OF ESTIMATING. 


Art. 19 


ORDER OF ESTIMATING RAILWAY BRIDGES 

I 


Truss Memb.-Web Diag. 
Web Yert. 

Bot. Chord . 

Top Chord 

Total Truss Memb. 

Pins, Pin Nuts. 

Shoes & Mas. Pis. 

Rollers & Frames. 

Int. Floor Bms. 

End Floor Bms. 

Int. Stringers. 

End Stringers. 

Stringer Pedestals. 
Stringer Cross Frames. 
Stringer Laterals. 

Bottom Laterals. 

Top Laterals. 

Portals—Rods—Knees. 

Top Struts. 

Sub Struts. 

Sway Rods—Knees. 

Top & Bot.Struts-Deck Br. 
Bot. End Struts. 
Longitudinal Struts. 
Castings; Lead. 

Bolts & Spikes. 


Timber ft. B. M. 

Furnished by. 

Placed by. 

Tie Plates. 

Specifications. 

Paint—Shop, Field. 
Material. 

Reaming. 

Inspection by. 
Transportation. 

Haul. 

Removal. 

Erection. 

Bid f. o. b. or Erected. 
Certified Check. 

Bond. 

Penalty. 

Time of Completion. 

Bid Due. 

Substructure. 


Total Iron & Steel. 




Art. 19. 


ORDER OF ESTIMATING. 


39 


I 

ORDER OF ESTIMATING HIGHWAY BRIDGES. 


Truss Memb.-Web Diag. 
Web Vert. 

Bot. Chord 
Top Chord 

Total Truss Memb. 

Pins, Pin Nuts. 

Shoes & Mas. Pis. 

Rollers & Frames. 

End FI.Bms .\ Hanger Pis. 
Int.Fl.Bms. I Lat.Con.&c. 

Sidewalk Brackets. 

FI. Bm. Hangers. 

Bot. Laterals ! Connections 
Top Laterals 1 Pins &c. 

Portals—Rods—Knees. 

Top Struts. 

Sub Struts. 

Sway Rods—Knees. 
FI.Bm.Knees—LowTnwses 
Top & Bot.Struts-Deck Br. 
Bot. End Struts. 
Longitudinal Struts. 

Steel Joist—I Bms. 

Facia, Curbs, 

St. Ry., Exp. Joints 
Castings. 

Bolts & Spikes. 


Lumber ft. B. M. 

Buckle Pis. 

St.Ry.Rails-furnished by 
Laid by. 

Hand Railing. 

C. I. Newel Posts. 

Cresting, Ornaments. 
Latticed Hub Guard. 

Wood Fence. 

Paving-Roadways & S. W. 
Specifications. 

Paint—Shop, Field. 
Material. 

Reaming. 

Inspection by. 

Freight. 

Haul. 

Removal. 

Erection. 

Bid f. o. b. or Erected. 
Certified Check. 

Bond. 

Penalty. 

Payment. 

Time of Completion. 

Bid Due. 

Substructure. 


Total Iron & Steel. 




40 


ORDER OF ESTIMATING. 


Art 19 


ORDER OF ESTIMATING STEEL BUILDINGS. 


Trusses—Main, Vent., Knees. 
Lean-to. 

Special. 

Hip & Valley Rafters, etc. 
Columns—Main. 

Clearstory. 

Crane. 

Lean-to. 

End. 

Floor. 

Struts—Latticed Eave. 

Side, End, Vent. 

Special. 

Ties—Bottom Chord. 

Special. 

Ventillator Knees. 

Roof Purlins—Main, Vent. 

Lean-to, Special. 
Purlins—Side. 

End, Gable. 

Finish Angles—Main Roof. 
Vent. Roof. 

Lean-to Roof. 

Rods—Rafter, Main, Vent., 
Lean-to. 

Bottom Chord. 

Side Sways. 

End Sways. 

Sag Ties. 

Anchor Bolts—Bolts, &c. 
Crane Girders—Brackets. 
Floor Girders—Joist. 

Floor Plate. 

Stairs—Tracks for Doors, &c. 
Total Steel in Bldg. 


Crane Rails-Clips & Fastenings 
Corrugated Iron —Roof. 

Sides. 

Ridge Cap—Flashing. 

Gutters—Down spouts. 

Slate, Felt, Tin, Cornice, &c. 
Louvers. 

Wood Purlins, Nailing Strips. 
Sheeting ft. B. M. 

Skylights—No. & size—Glazing 
Windows—No. & size—Glazing. 
Doors. 

Door Frames—Window Frames 
Skylight Frames. 

Railings. 

Circular Ventillators. 

Brick Walls & Foundations. 
Specifications. 

Materials. 

Paint—Shop, Field. 

Freight. 

Haul. 

Removal. 

Erection. 

Bid f. o. b. or Erected. 

Certified Check. 

Bond. 

Penalty. 

Time of Completion. 

Bid Due. 



Art. 20. 


SPECIFICATIONS. 


41 


20. Specifications. A specification is a set of rules for 
the guidance of the designer, the draftsman, the rolling mill, 
the shop, the erector and the inspector. It is a part of the 
contract 1 and all work is gotten out in accordance with some 
specification, and for bridges, generally in accordance with 
some standard specification. There are a number of bridge 
specifications which are published in pamphlet form for general 
use. 

The following are some of the most used specifications for 
steel railway bridges: 

“General Specifications for Steel Railroad Bridges” of the 
American Railway Engineering and Maintenance of Way 
Association. 

(( General Specifications for Steel Railroad Bridges and 
Viaducts,” by Theo. Cooper. 

ee General Specifications for Railway Bridges, by Edwin 
Thacher. 

<f General Specifications for Railway Bridge Superstruc¬ 
tures,” by The Osborn Engineering Company. 

<e General Specifications governing the Designing of Steel 
Railroad Bridges and Viaducts,” by J. A. L. Waddell. 

The general specifications for highway bridges usually in¬ 
clude specifications for electric railway bridges because bridges 
frequently serve both purposes. The following are some of the 
more important of these: 

e< General Specifications for Steel Highway and Electric 
Railway Bridges and, Viaducts,” by Theo. Cooper. 

“General Specifications for Highway Bridges,” by Edwin 
Thacher. 

“General Specifications for Highway Bridge Superstruc¬ 
tures,” by The Osborn Engineering Company. 

“General Specifications governing the Designing of High¬ 
way Bridges and Viaducts,” by J. A. L. Waddell. 

Most railroads have standard specifications of their own. 
Manufacturers also have specifications which they use when no 
other is designated. The “Manufacturers’ Standard Specifica- 


^ee u Engineering Contracts and Specifications," by J. B. Johnson, 
for a complete discussion of the subject. 



* 




42 SPECIFICATIONS. Art 20 

tions,” given in the various rolling mill hand books, covers only 
the material as rolled. 

Specifications for bridges carrying electric railways, 
adopted by the Massachusetts Railroad Commission, have been 
written by Prof. Geo. F. Swain. 

The building codes of the various large cities are supposed 
to govern the design and erection of all buildings within their 
limits, but many of these are antequated and cannot be applied 
to modern types of construction. 

“General Specifications for Steel Roofs and Buildings,” by 
Chas. Evan Fowler, refers only to mill building construction. 

There are many points of similarity in all specifications, 
especially with regard to certain details. The tendency in the 
future will, no doubt, be towards more uniformity in all re¬ 
quirements for structures of the same kind. There is no more 
profitable study for the beginner, than the study of a number 
of standard specifications. 1 They give, among other things, the 
types of bridges to be used for different spans, clearances re¬ 
quired, construction of the floor, loads to be used in calculating- 
stresses of all kinds, unit stresses which must not be exceeded, 
details of construction such as lacing for compression members 
and rollers for expansion bearings, kind of workmanship re¬ 
quired, quality of steel and timber to be used, requirements as 
to painting, inspection, testing, etc. 

21. Stress Sheets and General Plans. These are made 
on tracing cloth and of some standard size. Each company 
usually has at least two standard sizes of drawings. The com¬ 
mon sizes are 8V 2 in. x 14 in., 11% in. x 18 in., and 24 in. x 
36 in. 

The stress sheet should show, on a single line diagram, 
stresses, make up of each member and its area, principal dimen¬ 
sions such as span length, panel lengths, depth and width, and 
complete general data. Live and dead load stresses should be 
given separately if the unit stresses are different. The maxi¬ 
mum shear and maximum moment should be given for plate 
girders. It is also well to specify the pitch of rivets in the 

Tor a comparison of the main features of a number of railway 
bridge specifications, see an article by Prof. A. H. Heller in “Engi¬ 
neering News,” Vol. 50, page 444. 



Art. 21. 


STRESS SHEETS AND GENERAL PLANS. 


43 


flanges of girders, and the number of rivets required in the end 
connections of floor beams and stringers. (See stress sheets Figs. 
35, 53 and 166.) 

Full general data should be given for reference in examin¬ 
ing the structure after it has been in service for some time and 
when it may be overloaded. Under this head are included the 
specifications governing the design, the kind of steel, the location 
of the structure, the live and dead loads assumed, the grade, 
the alignment, the skew (if any), the construction of the floor, 
the distance from masonry to bridge seat, etc. 

For bridges, the diagrams usually include an elevation, a 
half or full view of the upper and lower lateral systems, an end 
elevation and a cross section. 

General plans may be simply “show” plans or plans giving 
more or less detail. The latter sometimes show practically every¬ 
thing except the rivet spacing and lengths of details. 


CHAPTER III. 


MANUFACTURE AND ERECTION. 


22. Shop Operations. Before taking up the subject of 
shop drawings, we will consider, briefly, the method of proceed- 
ure in the shop work and the erection. This description will be 
general, as all classes of work are not handled alike and various 
plants differ somewhat in their equipment and methods. 

When the shop drawings on a contract are complete, blue 
prints of them and the accompanying bills of material are sent 
to the various departments of the shop. In the templet shop , a 
wooden templet is made for each constituent piece of each dif¬ 
ferent member* excepting, of course, such parts as rods, eye 
bars, pins, rollers, etc. This templet is of the exact length (or 
half length) of the finished piece, gives bevels and has holes 
at every point where a rivet hole is to be located. It is to be 
clamped to the metal for the purpose of laying out the work 
to be done on each piece. Laying out directly upon the metal 
is seldom done because of the danger of making errors and ruin¬ 
ing the steel for the purpose for which it was intended. 

When the steel arrives from the mill it is unloaded at one 
end of the plant and marked with the contract number and 
sizes for future identification. Pieces of the same size are piled 
together and separated from other sizes as far as possible, so 
that any material can be gotten out easily at any time without 
handling other material which is not wanted. The unloading 
is usually done with a crane of some sort which deposits the 
material in the yard, or at some plants, in the shop. 

When enough material on any contract has been received 
from the mill and that contract is reached on the shop pro¬ 
gram, the material is run into the shop as it is needed, and us¬ 
ually continues straight through to the opposite end of the plant 
where the finished product is loaded. 

The first operation after the material is run into the shop 
is to straighten it so that the templet may be applied and that 
all pieces may be laid out accurately. This is clone with presses, 
rolls and sledges. The next operation is laying out , that is, 


44 


Art. 23. 


ERECTION. 


45 


marking the lines on which the material is to be sheared, and 
with a center punch, which fits closely in the holes in the temp¬ 
let, the position of each rivet hole. Some material is sheared 
to length first and then laid out. From the shears or laying out 
skids, the material passes to the punches where all holes for 
rivets are punched. Next the various pieces which are to be 
riveted together are assembled and fitted, putting enough bolts 
through the rivet holes to hold the pieces in position until the 
riveting is completed. These bolts are taken out at the riveting 
machine as the riveting progresses. Before the pieces are as¬ 
sembled, such faces as will be inaccessible after riveting are 
painted, and before the riveting is done the holes are reamed out 
to correct inaccuracies in punching, or if reaming is required 
it is done at this time (2). Some pieces require planing, boring, 
chipping and hand riveting after the power riveting is done. 

After all the operations have been performed on a piece, 
it is run on to a scale and weighed by the shipper, who makes 
out a shipping bill. Having been weighed and inspected to see 
that it conforms with the drawing it is painted and loaded upon 
cars or stored to go out when wanted. 

All bending, forge work, upsetting, etc., are usually done 
in the blacksmith shop. Turning, planing (except rotary plan¬ 
ing) and all machine work are done in the machine shop. 

23. Erection. Putting up the work in the held may be 
a very simple operation or one involving the use of a large 
plant and considerable risk, depending upon the character of 
the structure and its location. 

Bridges are usually erected on false work, which consists of 
wooden trestles, by means of a traveler or gallows frame, to 
which the tackle for hoisting all material into place is fastened. 
A gallows frame consists simply of two wooden posts connected 
together at their tops by a beam and braces. The posts usually 
rest upon temporary stringers outside of the line of the girders 
or trusses. A traveler has four legs, at least, braced together 
longitudinally and transversely allowing room enough under it 
to erect the bridge inside of it. It runs on wheels so that it may 
be moved lengthwise of the bridge as the erection progresses. 

Generally during the erection of railroad bridges the traffic 
must not be interfered with, but trains usually reduce their 


46 


THE DRAFTING DEPARTMENT. 


Art. 24 


speed and run slowly over a bridge which is being renewed. The 
floor system is sometimes put in place before the trusses and 
blocked up somewhat higher than its final position. The trusses 
are erected beginning at the center, putting up one half and 
then moving the traveler back to the center and working toward 
the other end. Enough bolts are put into the connections, which 
are to be riveted, to fill about two-thirds of the holes. After 
everything is connected together, the bridge is “swung that is T 
the blocking between it and the false work is taken out and it 
becomes self-supporting. Rivets for connections of tension 
members of trusses are driven before the bridge is swung and 
all others after it is swung. 

In the designing and detailing of steel structures it is im¬ 
portant that the manner of erecting them be constantly kept in 
mind. Field splices must be placed in the proper positions, 
connections should be designed with a view to facility in mak¬ 
ing them under the conditions which obtain in the field; field 
rivets should be located where they can be easily driven; suffi¬ 
cient clearance must be provided at all joints. All pieces should 
have plain marks for identification and a good erection diagram, 
showing all marks, should be made. 1 

24. The Drafting Department. The organization of the 
drafting department in various companies differs greatly. 
Usually there is a chief draftsman who has general supervision 
of all work and assigns the work to the various men under him, 
whom he deems best fitted to get out the drawings for it. Gen¬ 
erally a contract is given to a squad foreman, who has three or 
four men working under him and who directs the method of 
getting out the work, writes the order bills for the material, and 
sometimes makes some of the more complicated drawings. When 
the drawings are made and traced they are sent to a “checker” 
who is generally an old experienced draftsman, and he checks 
every dimension and size given on the drawing and marks such 
changes as are necessary, in pencil. The drawing is then cor¬ 
rected by the one who made it, and after being accepted and 
signed by the checker is ready to send to the blueprint room. 

^or details of tools, tackle, traveler, false work, etc. see Chapter 
XIII in Du Bois’ “Framed Structures, 11 by John Sterling Deans, M. Am. 
Soc. C. E., and Appendix C in Johnson’s “Modern Framed Structures. 1 ' 



Art. 25. 


A DRAFTSMAN’S EQUIPMENT. 


47 


The man who makes the drawing and the checker are held 
equally responsible for any errors. 

Drawing hoards should be used, as it is very inconvenient 
to have to remove a tracing from a table top in order to make 
a lay out or to work a short time on another drawing. The draw¬ 
ing boards should be of pine so made that they will not warp 
or split. They should have one true edge, preferably of hard 
wood, at the left hand end. 

T-squares should have rigid heads and true edges. 

The drawing table should be large enough to accommodate 
the drawing board, reference drawings, etc. It should be at 
least six feet long, and supplied with a drawer for instruments, 
etc. It should be, preferably, adjustable as to height and slope 
of top. The stool accompanying it should be adjustable for 
height. 

The lighting of the drawing room should, of course, be the 
best possible. If artificial light is used at any time, it should be 
a diffused light reflected from the ceiling. A comparatively 
quiet, well ventilated, clean and orderly office will be conducive 
to good work and little friction. Unfortunately all of these 
reasonable conditions are not usually obtained. 

A suitable filing system should be provided for all drawings 
and other data, preferably in a fire proof vault. 

25. A Draftsman’s Equipment. Shop drawings are the 
working drawings used in the shop and give all details. Making 
shop drawings is the foundation upon which a bridge engineer’s 
future advancement is based. A draftsman makes his own 
reputation. Conditions have been such in the past that advance¬ 
ment comes to the draftsman about as rapidly as he is able to 
take advantage of his opportunities. One who makes himself 
thoroughly acquainted with the theory of everything he does, 
one who is not afraid of a little work outside of office hours, who 
carefully studies and considers every piece of work entrusted to 
him, will not find the work growing monotonous. A reputation 
for making mistakes is perhaps the worst a draftsman can make 
for himself. The fact that every drawing is checked should 
have no influence upon the amount of care bestowed on it. 
Errors will sometimes pass the checker and are expensive in 
nearly all cases. Errors are especially liable to occur when 


48 


A DRAFTSMAN’S EQUIPMENT. 


Art. 25 


changes are made necessary after a drawing is made, either 
before or after it is checked. For this reason a draftsman should 
do everything according to some method. There is a best place 
to begin on a structure and a most logical order in which to 
work it up, not only each drawing but every detail. If this is 
followed very little erasing will have to be done, and everything 
will be better designed than if one detail is worked out regard¬ 
less of everything else and afterwards fudged to correspond 
with other requirements. After changes are made the drawing 
is usually out of scale, and not drawing to scale is usually con¬ 
ducive to mistakes. Even rivet heads should he to scale. 

Every drafting room has some peculiar practices of its 
own, and it is generally the part of wisdom for a new-comer to 
conform with them as soon as he can find out what they are. 

A draftsman’s outfit should include the following tools : 

1st. Triangles, ruling pen, compass, bow pen, bow pencil, 
dividers large and small, pen knife, pen wiper, scales, oil 
stone, etc. 

2nd. A copy of some rolling-mill’s handbook. 

3rd. Tables of squares and longarithms of dimensions in 
feet, inches and fractions. 

4th. A copy of the office standards. 

5th. A five place table of the natural functions of angles 
varying by minutes. 

6th. A five place logarithmic table of numbers and func¬ 
tions of angles. 

7th. A slide rule. 

8th. Reference books. 

9th. The following which are usually supplied by the 
office: drawing tables, drawing boards, T-squares, erasers, soap¬ 
stone, pencils, pens, tacks, tracing cloth, drawing paper, ink, 
and chalk. 

The drawing instruments should be of the best quality. 
Loss of time due to poor instruments is inexcusable. Triangles 
should be transparent and not less than inches thick. A 
5 in. or 6 in., 45 degree triangle and an 8 in. or 10 in. 30-60 de¬ 
gree triangle will be found convenient. For some classes of 
work a quarter pitch triangle (slope 1 in 2) and a small triangle 
that will fit the standard bevel of the flanges of I-beams and 


Art, 25. 


A DRAFTSMAN’S EQUIPMENT. 


49 


channels (1 in 6) will save time. The ruling pen should be of 
a kind that is easily cleaned because the ink used dries rapidly. 
There are pencil sharpening machines which do very good work. 
If there is not one conveniently located in the office, a sharp pen 
knife can be made to do good work in connection with a piece 
of sand paper or a file for sharpening the lead. A draftsman 
who wishes to make a workmanlike drawing will not work with 
a blunt pointed pencil. 

The architects’ scale is used for all shop drawings. This is 
a scale of feet and inches. Scales should not be over 6 inches 
long for detail work and preferably have white celluloid faces. 
A long scale necessitates moving the T-square and triangles too 
much. A 12 inch decimal scale for longer dimensions and 
graphic calculations should also be provided. A triangular ar¬ 
chitects’ scale is usually divided into the following scales per 
foot: 3-32 in., V 8 in., 3-16 in., % in., % in., y 2 in., % in., 1 in., 
iy 2 in., 3 in. and 12 in. or full size. As most of these scales are 
used infrequently, it is more convenient to have two flat scales 
covering the more often used scales. One divided into scales 
of y 8 in., 14 in., y 2 in. and 1 in. per foot and another divided 
into % in., % in., 1V 2 in. and 3 in. per foot will answer most 
purposes. A scale of l 1 /^ in. per foot makes a very nice scale 
for some classes of work but it is not a standard scale. The scale 
of 14 in. per foot is much used by architects. 

A good pencil eraser, one that will not “smear,” is, of 
course, necessary. Ink on tracings should be erased with a 
rubber ink eraser although a steel eraser (knife) may be used 
occasionally. To prevent ink “running” and dirt accumulating 
on the spot which has been rubbed, the tracing cloth should be 
rubbed with soapstone. To confine the rubbed surface within 
the required limits, it is convenient to have a thin metal erasing 
shield with holes and slots of different sizes. 

The ink should be waterproof india ink of good quality. 

For drawing lines on detail paper a 6H pencil should be 
used, because it does not require such frequent sharpening as a 
softer pencil. For putting in dimensions and figures a 411 pencil 
will be about right. On tracing cloth a 3H pencil will work best, 
and a soft pencil is needed for scratch figuring. 

A pen must be “broken in” before good lettering can be 


50 


A DRAFTSMAN’S EQUIPMENT. 


Art, 25 


clone with it. After it 'has been used for some time the point 
becomes blunt and may be improved by using a knife on it as 
on a pencil in sharpening it. 

The rolling-mill hand books contain much information of 
use to the draftsman, and he should know what may be found 
in them. The pages most frequently referred to should be in¬ 
dexed for quick reference in some manner similar to a ledger 
index. The principal shapes rolled by the various mills are all 
alike and in accordance with the standard adopted by the Manu¬ 
facturers’ Association. All properties of these shapes are given 
in the hand books. The American Bridge Company’s Stand¬ 
ards give much other valuable information. 

Each office usually has a set of standard tables and draw¬ 
ings. Many of these are of general value, but some correspond 
with certain local shop practices. 

Tables of squares and logarithms of dimensions in feet and 
inches are in constant use, and are a much greater help than 
would appear on first thought. 1 In working with right angle 
triangles, only the table of squares is necessary. The table of ' 
logarithms is not used so often, but when there is use for it 
it saves much time. These tables give results to the nearest 1-32 
of an inch, and this is the smallest fraction ever used on struc¬ 
tural steel drawings. 

The above tables, together with a good table of the natural 
functions of angles such as is given in Trautwein’s Pocket- 
. book, and a five place table of logarithms such as Gauss’s or 
Jones’ will enable the draftsman to solve all problems in men¬ 
suration which may arise, if he is thoroughly familiar with the 
fundamentals of geometry and trigonometry. 

The draftsman should be familiar with the use of the slide 
rule, and should use it to calculate pins, rivets, bearings, etc. 
(18) If the office is provided with a Thacker Cylindrical Rule 
it may be used to good advantage in calculating the dimensions 


lu Tables of Squares by John L. Hall and “ Buchanan's Tables of 
Squares by E. E. Buchanan, give the squares of dimensions under 
50 feet, expressed in feet and inches. Tables by-Thos. W. Marshall 
give the logarithms of the same quantities. “ Smoley's Tables of 
Squares ond Logarithms,” by Constantine Smoley, give both the 
squares and logarithms of these dimensions in parallel columns. 



Art. 26. 


ORDERING MATERIAL. 


51 


in oblique triangles, and will give results within 1-32 of an inch 
so long as none of the lengths involved exceed about 30 feet. 

A note book is very convenient for keeping calculations 
which one may wish to refer to again. Many figures which a 
draftsman makes will be on scratch paper, but all figures which 
may be needed for future reference and for consultation when 
the changes made by the checker are gone over, should be kept 
in a permanent and methodical form. A careful man will find 
satisfaction in seeing how he made a mistake, and this record 
will also be valuable in giving reasons for certain things he has 
done, and prevent his being misled by some one who, perhaps, 
has not considered all the conditions. 

A draftsman should have at hand reference books in order 
that he may look up any point in theory with which he is not 
familiar. A few may be mentioned here but, of course, for 
structures out of the ordinary special works should be consulted. 
The most useful are: 

Johnson’s “Theory and Practice of Modern Framed Struc¬ 
tures,” Heller’s “Stresses in Structures,” some good work on 
the strength of materials, Wright’s “The Designing of Draw 
Spans,” Freitag’s “Architectural Engineering,” Merriman and 
Jacoby’s “Bridge Design” (Part III of Roofs and Bridges), 
Kent’s “Mechanical Engineer’s Pocketbook,” Trautwein’s 
“Civil Engineer’s Pocketbook,” Engineering News, etc. Access 
to the Transactions of the American Society of Civil Engineers, 
and of other engineering societies will be valuable. An indivi¬ 
dual card index should be kept in order that any subject may 
be looked up when occasion requires. 

26. Ordering Material. As soon as a contract has been 
secured and entered, complete data relating to the construction 
are turned over to the drafting department. The first thing to 
be done by this department is to prepare a list of the material 
required, which is called an “order bill.” The draftsman to 
whom this is entrusted should first care.fully examine all data. 
If any necessary information is found lacking at any point in 
the progress of the work, it should be promptly reported. Care 
should be taken to include everything in the order bill that will 
be required to make the structure, unless upon inquiry it is 
found that certain materials may be ordered later. 


62 


ORDERING MATERIAL. 


Art. 26 


Since the order bill must, in general, include all details such 
as pin plates, batten plates, lacing bars, rollers, pins, eye bars, 
rods, timber, lead, corrugated iron, windows, doors, crane run¬ 
way rails, etc., it is necessary to proportion all details, to calcu¬ 
late pins, rivets, bearings and connections, and to determine 
clearances, splices, etc. In some cases considerable drafting 
will be required, but not nearly so much as will be necessary to 
make complete detail drawings. In general, this preliminary 
drafting should be done so that after the order bill is complete 
the drawings may be developed into final shop drawings. This 
method will save much drafting, which is expensive work. 

In order to expediate the placing of the orders for the ma¬ 
terial at the mills, no more drafting than necessary should be 
done. It may be supplemented by free hand sketches and notes, 
which should be preserved with other data for reference by the 
checker and draftsman making the shop drawings. 

For a contract of any magnitude the order bills would be 
gotten out in sections; those parts which will be needed first 
should be gotten out first. In any case, the first attention should 
be given to the kind of material which will be most difficult to 
get promptly. 

However, time spent upon a consideration of the entire con¬ 
tract in all its bearings, and especially with regard to duplica¬ 
tion of parts, is never wasted. 

The order bills are checked and a copy sent to the order 
department. The originals are retained for the guidance of the 
draftsmen who make the shop drawings. The element of time 
is so important that most companies do not make blue prints 
of the order bills but use some more rapid duplicating process. 

The order department makes up a “mill order” from the 
order bills, bringing together all items of the same kind and 
combining some of the shorter lengths into long lengths (mul¬ 
tiple lengths) to be sheared to the proper lengths at the shop. 

Some companies keep more or less material in stock in 
order to be able to make prompt deliveries of certain classes 
of work. In this way considerable waste (short pieces) accumu¬ 
lates, which must be applied on contracts whenever an oppor¬ 
tunity offers. It is the duty of the order department to keep 
track of the stock, to keep up the supply of stock sizes, and not 


Art. 26. 


ORDERING MATERIAL. 


53 


to allow an accumulation of waste. When stock material is ap¬ 
plied to a contract it should be so marked, in order that it may 
be reserved. The shop hill generally shows what items are to 
come from the mill and what items from stock. Stock material 
cannot always be used on contracts, as some specifications re¬ 
quire a different quality of material from that carried in stock 
and require inspection at the mills. 

The importance of avoiding errors and omissions in the 
order bills is apparent, since they may cause serious delay to the 
entire work. 

In making up the order bill, it should be remembered that 
odd sizes of angles and other shapes should be avoided in order 
to get prompt delivery from the mill. % inch extra material 
should be ordered for all tool finished (milled or planed) sur¬ 
faces, except for the flat surfaces of plates for which 1-16 in. or 
% in. extra should be ordered, depending upon the size of the 
plate. Stiffener angles which are to be crimped or offset, are 
usually ordered as long as the depth back to back of angles of 
the girder to which they belong. The length of bent angles and 
plates is taken on the center of gravity line. Other material is 
ordered the exact length required (avoiding smaller fractions 
than eighths of an inch) and usually comes a little longer so 
that it may be sheared to the finished length. 

Plates are of two kinds, “sheared” and “universal mid ” 
The former have sheared edges and the latter rolled edges. The 
maximum width of universal mill plates varies from 20 in. to 
4S in., depending upon the mill where they are rolled. In the 
rolling mill handbooks will be found tables showing the maxi¬ 
mum length to which plates of various widths and thicknesses 
can be rolled. Plates up to 7 in. in width are called bars. Flange 
plates for plate girders are usually obtained as long as wanted, 
but web plates must be spliced. It is usual to order web plates 
of a width in. less than the depth back to back of angles, and 
to allow 14 in. clearance between their ends. It is permissable 
to order odd shaped plates sheared to the dimensions wanted, as 
shown by a sketch. 

Angles may be obtained in single pieces up to about 90 feet 
long, provided that they do not weigh more than about 3,000 lbs. 
apiece. Special sizes should be avoided on account of slow de- 


54 


SHOP DRAWINGS. 


Art. 27 


livery. The order bill should indicate the kind of material 
(soft or medium) and the specifications governing its quality 
and inspection. 

27. Shop Drawings. Drawings should be made on the 
dull side of tracing linen, beca/use they will not lie flat when 
made on the smooth side. An experienced draftsman will work 
directly on the tracing cloth and this cannot be done except on 
the dull side. Drawings may be fastened to the board with 
thumb tacks, but it will be found more satisfactory to use very 
small carpet tacks, tacking the four edges like a carpet so that 
the drawing will be stretched and present as smooth a surface 
as possible. Changes in temperature and moisture of the air 
may sometimes necessitate restretching. The drawing should be 
covered up at night with a heavy cloth or a piece of table oil 
cloth. If the drawing is made on the tracing linen direct, the 
principal lines may be inked before the drawing is completed 
in pencil. This will bring out the main parts and make it more 
satisfactory to work with, especially if there is much work on 
the drawing, as the lines are liable to become faint from rubbing 
over them. It is, however, safer for an inexperienced man to 
make a complete pencil drawing before doing any inking. 

In order that the tracing cloth may “take” the ink it is 
necessary to rub it with pulverized chalk, Fuller’s earth, or 
blotting paper. This is especially necessary during cold and 
damp weather. 

The draftsman should not get the idea that the appearance 
of a shop drawing is of no importance. A drawing should have 
a workmanlike appearance or it will not inspire confidence in 
its correctness. The general arrangement and the lettering are 
the main features so far as appearance is concerned. All 
lettering should be free hand and the draftsman should, at the 
beginning, practice with exceeding patience some simple style 
of lettering. 

The style used in the drawings published in the Engineering 
News is a very good one to follow. A very important point is 
to have the letters and figures of different sizes, depending upon 
their importance. The sizes of materials should be more promi¬ 
nent than the rivet spacing, and center lengths than secondary 
dimensions. There is also a best position for each dimension. 


Art. 27. 


SHOP DRAWINGS. 


65 


I lte letters and figures should be made as carefully as is con- 
• sistent with rapidity. It is only practice, persistent and patient, 
that can make a good letterer. Not all can hope to become equally 
proficient, but all can improve. 

The general appearance of a drawing depends very much 
upon the general arrangement, the scale, and the relative sizes 
of letters. A drawing may cover practically all the available 
space within the border lines, if there is no evidence of crowding 
anywhere, and if the various parts or pieces represented stand 
out clearly so that the different views of the several pieces can 
not be confused. There is an advantage in compactness, but 
clearness is Hie first consideration. Not every one who uses a 
drawing can read it as readily as the man who made it. HE 
SHOULD MAKE IT SO PLAIN THAT IT WILL EXPLAIN ITSELF 
AND THAT ONLY GROSS NEGLIGENCE WILL ALLOW ANYONE 
TO MAKE A MISTAKE IN USING IT. 

The object should be not to make it “good enough’’ but to 
make it first class. 

The length of a structure, like a truss, seldom determines 
the scale of the drawing. Usually the available width of a sheet 
determines the scale to be used. If the structure is too long to 
show on one sheet to this scale two or more sheets may be used. 
The center line diagrams of trusses are usually drawn to a 
smaller scale than the details, say % in* or % in. per foot while 
the details would be 1 in. or 1 y 2 in. per foot. In this case, of 
course, there is a part of the member near the middle which is 
cut out and which need not be shown, but the spacing of rivets, 
etc., is indicated. True projections are not always made if they 
do not serve to make matters clear. Bottom views are seldom 
made but sections instead, placed below the elevation. The top 
view should always be above the elevation. A half top view 
and half section are sometimes made together when symmetry 
will allow. A single view or two views will sometimes suffice, ’ 
especially if it is a construction with which the shop is familiar. 
There should be no more drafting than is necessary for clear¬ 
ness. 

Drawings should have one or two plain border lines. If two 
are used the blue prints may be trimmed to the outer one. (See 
Pig. 24.) In some drafting rooms an outfit for printing titles 


66 


SHOP DRAWIXGS. 


Art. 27 


on tracings is used; in some rubber stamps are used. Printing 
is the most satisfactory method when the number of drawings 
turned out is large. Titles should correspond with some stand¬ 
ard as indicated in Fig. 24. The title should, when possible, be 
in the lower right hand corner. When necessary it may be 
divided in two parts placed side by side. A supplementary 
form for general information is frequently placed in the lower 
left hand corner as shown in Fig. 25. 

_ 36' _ # 

_ 35 ~^ _^ 

35" 


THE OHIO STATE BRIDGE CO. 
COLUMBUS. OHIO 

Bridge No. 34 Western Div. Q.R.&M.Ry. 

/ Through Truss Span 'Double Track.Skew 
126-6 C. to C. 

Floor Beams Stringers and 
Portals. 

In Charge of Smith 

Drawn by AJ.K 7-/-07 Revised 3-6-07 
Checked byyVT7-34-07 Revised 8-7-07 

Shop Bills Nos. 1,2.3 d 4 

CONT. NO. 746_ _@| 

_ f 7r/m B/ue Pr/nf on th/s L/neJ _ 

(7r/m Tracirr on this Line) 

Fig. 24. 

Dimension lines and rivet gage lines should be very fine 
and preferably made with black ink. They are sometimes made 
with red ink, but the ink should be of known quality in order 
that it may not run or spread with age. Center lines which 
form one end of a view should be heavy dot and dash lines; 
other center lines should be fine lines. No shading is attempted 
on shop drawings except to show curved surfaces. 

All lines of dimensions should connect completely with the 
centers, and there should be separate lines for center distances, 
rivet spacing, lacing spacing, etc. 


"N 














Art. 27. 


SHOP DRAWINGS. 


57 


Rivets connecting lacing bars to compression members 
should stagger with those in the web of the member. The end 
bars should connect to the first rivet in the batten plate or one 
not over 5 in. from this rivet. Batten plates should be made of 
such widths as will fit the spacing of the lacing and meet the 
requirements of the specifications. 


36' 


35i. 


35 / 


Specifications - Cooper’^Ry. /90/. 
Materia/ Soft O H. Steel, 
ftivefe g f/o/es Unless otherwise noted. 
Meant inp - none. 

P/aninp sheared ec/pes - none. 

Shop Paint- /Caa/MectLeac/. 


*0 

(M 


N«4 

<\l 


M 


Fig. 25. 


Dimensions which determine clearances for field connec¬ 
tions, the position of open holes, etc., should be given in such a 
manner as to be convenient for the inspector. It should not be 
necessary for him to add rows of figures. If the inside distance 
at the end of a member is the important one for clearance, that 
should be given. If the member is to be entered inside of an¬ 
other, its outside width should be given. In some cases both are 
necessary. 

For identification in the drawing room, shop and field, each 
piece should have a mark. All pieces which are exactly alike* 
should have the same mark. The marks should all appear on 
the general marking diagram, or erection plan, which shows the 
relative location of all the pieces by their marks. 

Under the drawing of each piece the number required 
should be plainly given together with the numbers which are 
to be right and left, thus, 

2 Right Girders Req. Mark G R (shown) 

2 Left Girders Req. Mark G L. 
















58 


SHOP DRAWINGS. 


Art. 27 


The system of marking, for each kind of structure, should 
be standard as far as possible. For example, U might always 
stand for upper, L for lower, P for portal, V for vertical, D for 
diagonal, B for bracket, S for stringer, F for floor beam, etc. 
Marks should be as simple as possible, and preferably consist of 
capital letters and figures, avoiding primes and subscripts. To 
insure shipment, small pieces which the drawings show bolted 
to large ones, may be given separate marks and noted on the 
shipping bill. 

Steel in section is shown by uniform cross hatching or in 
black. See Figs. 26, 28, and 29. Other kinds of material are 
seldom used except for draw-bridge machinery. If some con¬ 
vention is adopted for each kind of material, it will serve to 
make the drawing clearer. 

It is well to follow some conventions. If a member is ver¬ 
tical in a structure, it should be drawn with its axis parallel 
with the sides of the drawing unless this would necessitate the 
use of too small a scale, in which case it may be drawn parallel 
with the top of the drawing, with the top of the piece at the 
right. Inclined members, when not shown in their natural posi¬ 
tion, should be drawn lengthwise of the sheet. 

Notes may be used when they will save considerable draft¬ 
ing, but should generally be avoided. Making the drawing com¬ 
plete will guard against mistakes in the office and the shop. 
A note should he so worded that its meaning cannot possibly he 
mistaken. It is not permissable to refer to a reference; the 
drawing referred to should give full information. In any case 
each drawing should give sizes of all material, pin sizes, center 
dimensions, and other important information. 

Duplication in details, in spacing, in parts of members and 
in members is very important. The number of templets is bv 
this means reduced to a minimum. It is permissable to use a 
little extra material to obtain duplication in some cases. When 
two members differ but slightly from each other, one drawing, 
with proper notes, will answer for both. If two drawings are 
necessary and -some parts of one are the same as for the other, 
it is better not to repeat the rivet spacing but to refer to the 
other drawing, as this will call attention to the fact that there 
is a duplication of templets. A templet is frequently made to 


Art. 27 


SHOP DRAWINGS. 


59 


answer for two different pieces by putting into it all the holes 
for each piece and marking one set of holes in some way to 
distinguish them from,the other set. 

Rivet Spacing should be as regular as possible. All rivet 
heads need not be shown but they should not be omitted at the 
ends of members, where clearances are important, in pin plates, 
or where countersinking or flattening are needed. Field holes 
should always be shown blackened, and it is generally a good 
thing to show them in at least two views. The conventional 
signs for countersinking and flattening (See Fig. 20) should be 
made very plain lest they be confused with dimension lines. No 
countersinking is allowed in the tension flanges of stringers, 
floor beams or girders. All countersinking should be avoided 
in long pieces since it involves an extra shop operation and long 
pieces are expensive to handle. 

All open holes should be so located that the field rivets 
may be easily driven. Rivets are driven from the sides or from 
above, never from below. It is not good practice to put two 
consecutive rivets on the same line in an angle having two gage 
lines, except for purposes of symmetry, and when it cannot be 
avoided, as in the connection of a floor beam to a girder. 

Punching of holes of different sizes in the same piece should 
be avoided as much as possible, especially in long pieces, because 
it requires extra handling. Avoid two or more shearings at the 
end of an angle or the edge of a plate when one will answer 
just as well. Projecting corners should, however, not be al¬ 
lowed. Whenever a reentrant cut has to be made, there should 
be no sharp angle but a curve. 

In giving dimensions over 9 inches the feet and inches 
should generally both be given, thus O'-ll", 3'-7". All dimen¬ 
sions over one foot, except the widths of plates, should be given 
in feet and inches; width of plates are always given in inches, 
thus, 1—37"X%"X3'—6%". The longer leg of an angle should 
be given first. Rivet spacing should not be given by repeating 
a number of consecutive spaces that are just alike, but should 
be indicated as follows: 

8 spaces at 3"=2'—0" 

8 alternate spaces at 1'—3"=10'—0". 


60 


SHOP DRAWINGS. 


Art. 27 


Unless the stringers rest on the bottom flange of the floor 
beam, shelf angles should be provided for them to rest on for 
convenience in erecting. Where stringers rest on the bottom 
flanges of the floor beams, and where inside splice angles are 
used, they should be ground to fit the fillet of the flange angle. 

If angle laterals are used, which have lugs riveted to them, 
it is easiest to make the back of the angle the center line. 

It should be remembered that angles are not exactly of the 
nominal size, but that the length of the legs overruns, except for 
sizes rolled in finishing rolls. Making fillers and splice plates 
14 inch shorter than the nominal distance between flange angles 
will not always answer. 

Entering connections should be avoided. They make erec¬ 
tion expensive and are liable to result in injury to the material. 

Wherever two or more members come together, clearance 
should be allowed if possible. The thickness of an eyebar head, 
if figuring clearances, is always taken T V inch greater than the 
nominal thickness. A total further clearance of 14 inch to % 
inch is allowed where several members enter between the sides 
of another, the amount depending upon the members so enter¬ 
ing, the number of pin plates, etc. Pin fillers are, for the same 
.reason, made *4 inch shorter than the space they are to fill. 

Projecting plates should not be riveted to large pieces, but 
shipped loose. It is better to drive a few more rivets in the 
field than to have these details broken off in shipping and hand¬ 
ling, or have them interfere with the handling of heavy pieces. 
Lateral plates for plate girder spans may be riveted to one of 
the laterials connecting to them if the laterals are not too long. 

Care should be exercised so that no part of the lateral sys¬ 
tem will interfere with the floor construction or the masonry. 

It is important to know in what order the spans of a via¬ 
duct will be erected and to arrange the details at the tops of 
the columns so that each span may be put up independently. 

Holes for anchor bolts must be so located that the masonry 
may be drilled after the steel work is in place. 

At panel points, not only those rivets which come opposite 
a member in its final position should be flattened or countersunk 
for clearance, but also enough to allow the members to be easily 
assembled. Batten plates should not come too close to a diago¬ 
nal member. 


Art. 27. SHOP DRAWINGS. 61 

Top chord splices should come opposite each other in the 
two trusses, and the sections nearest the center should extend 
over at least two panel points so that in erection this panel will 
be self-supporting. It should be remembered that the traveler 
must be moved and cannot generally support pieces except for 
about one panel length. 

There are two general methods of making shop drawings. 
First, a structure or part of a structure may be drawn showing 
all parts assembled in their proper relative positions. A bridge, 
for example may be drawn showing the truss members (usually 
half of one truss for a square span) in the relative positions in 
which they belong, while a separate drawing is made of each 
of the other pieces such as floor beams, portals, etc. This method, 
of course, is not adapted to some things, like floors and columns 
of office buildings. Second, each kind of piece belonging to a 
structure is drawn separately and complete in itself. In the 
case of a truss for example, this necessitates the making of a 
layout of each joint beforehand, in order to determine clear¬ 
ances, and the fitting together of the parts. This method re¬ 
quires more drafting than the first, and is therefore more expen¬ 
sive. The first method is nearly always used for bridge and roof 
trusses unless the depth is so great that it would necessitate too 
small a scale. 

At some plants the templet shop is arranged to permit lay¬ 
ing out a structure full size. The templet maker locates the 
rivets which are shown but not exactly located on the drawing. 
Where this is practiced drawings are made in a somewhat dif¬ 
ferent manner, as to what dimensions are given, than where all 
details including rivet spacing are shown. 

The beginner should always have a sample of the kind of 
structure of which he is required to make a drawing, for a 
guide. There are many practical points which can only be 
picked up in this way. He should also make himself familiar 
with the machines in the shop and their capacities. It is some¬ 
times as easy to design a masonry plate which will go into the 
planer as one that is too wide for it. 

Before starting on the drawings for any particular struc¬ 
ture, a draftsman should make himself perfectly familiar with 
all the data. Time spent in a general preliminary consideration 


62 


ORDER OF PROCEDURE. 


Art. 28 


and plan of action is generally well spent. If further informa¬ 
tion is required, it should be asked for at once. If a mistake or 
omission is discovered in the order bill, the attention of the 
engineer in charge of the office, or of this particular contract, 
should be called to it at once. 

Working to the order bill may make some trouble, but this 
is necessary. Should any doubtful points come up, some one 
should be consulted who is more familiar with this kind of work, 
or with the requirements of the parties for whom the work is 
to be built. A man should never he ashamed to ask intelligent 
questions. 

i 

28. Order of Procedure for a Pin Connected Bridge. 

No definite order of procedure can be outlined, which can be 
followed in all cases, but the following order for a pin connected 
truss bridge will serve as a guide to the beginner. 

The stress sheet and specifications form a part of the con¬ 
tract and the draftsman must work from these. 

1st. Write on a blue print of the stress sheet the horizontal 
and vertical components of the stresses in the inclined members. 

2nd. Determine the location of the centers of gravity of 
the compression members and decide on the location of the 
center lines. 

3rd. Determine all the center lengths so as to give the 
required camber. 

4th. Make a table of heights as follows: 

Depth of tie over the stringers = 

Depth of the stringers = 

Bottom of stringer to Bot. of FI. Bin. — 

Bottom of Floor Bm. to Pin Cent. — 


Base of Rail to Pin Cent. 

Pin Cent, to Masonry 

Base of Rail to Masonry 

*/ 

Lower Pin Cent, to Base of Rail 
Required Clearance 

Lower Pin Cent, to Clearance 
Depth of Truss C. to C. Pins 

Depth of Portal, Vert, from P. C. 


— (Sum) 


= (Sum) 


— (Sum) 


= (Diff.) 






Art. 28. 


ORDER OF PROCEDURE. 


68 


5th. If the bridge is on a skew, calculate the lengths and 
bevels necessary to draw the portal. 

6th. Calculate the size of masonry plate required so as 
not to exceed the allowed pressure on the masonry and so as to 
provide enough room for the rollers. 

7th. Assume sizes of pins, determine thicknesses of pin 
bearings on each member and calculate the pins. When the pins 
are all calculated decide upon two or three sizes for the truss, 
making some larger than necessary for the sake of simplicity. 
Fix on the location and thicknesses of all pin plates and the 
number of rivets required in each. The calculation of the pins 
will have determined the packing at each panel point. 

8th. Calculate the pitch of rivets required in the flanges 
of the stringers and floor beams and the number of shop and 
field rivets for their end connections. (This information is 
frequently given on the stress sheet.) (21) 

9th. Calculate the rivets required in the lateral systems, 
including portals, to take the longitudinal and transverse com¬ 
ponents of the stresses as required. 

While performing the above preliminary work, a few 
sketches will be necessary, and it is important to decide upon 
the form of the connections for the lower lateral system, allow¬ 
ing clearances for eyebar heads, and to see that the steel work 
will fit the masonry, allowing sufficient clearance at the ends for 
expansion. 

No rigid rule can be laid down for the best order in which 
the different parts should be drawn up, but for this class of 
structure the following will work out satisfactorily: 

The scale for the center line diagram is usually % inch, H 
inch or % inch per foot, and for the details. % inch, 1 inch, 
11/4 inch or 11/ 2 inch per foot. The 1 inch scale is used more 
than any other one for details. 

1st. Draw the portal, especially if it is a skew bridge. A 
layout of the hip joint will be necessary. 

2nd. Work out the hip joint with portal connection, lat¬ 
eral connection, pin plates, etc. 

3rd. Work out the shoe joint with rollers, anchor bolts, 
masonry plates, shoes, end strut or beam and lateral connections, 
pin plates, etc. 


64 


ORDER OF PROCEDURE. 


Art. 28. 


4th. Work up the spacing of the lattice bars, batten plates 
and rivets in the end posts. 

5th. Work up the lower chord joints, with floor beam con¬ 
nections, beginning at the middle of the truss and working to¬ 
ward the end. 

6th. Finish the hip vertical. 

7th. Draw the top chord joints, and fix spacing for lattice 
bars, batten plates and rivets in top chords. 

8th. Finish the intermediate posts. 

9th. Finish the top view of top chords. 

10th. Draw top lateral system and top struts. 

11th. Draw bottom lateral system and end struts. 

12th. Draw stringers and beams. 

13th. See that each drawing has a proper title and number, 
and that all general notes required are on the drawings. 

14th. Go over each drawing to see that all information 
which may be wanted by the following persons, is given: The 
checker, the templet maker, the layer-out, the fitter-up, the in¬ 
spector, the shipper, and the erector. See that each piece is 
properly marked and the number wanted is given, that the sizes 
of rivets and open holes are all given. 

15th. Make a marking or erection diagram' (single line) 
and a diagram showing how the bridge is to be located on the 
masonry. 

16th. After the drawings are checked, look into all correc¬ 
tions carefully before doing any erasing. Do not erase the 
checker's marks. In case you do not understand the checker’s 
changes or see any reason for them, ask him for information. 
The important thing is to have the drawing clear and correct. 

Riveted truss bridges can be handled in much the same way 
as pin connected bridges. The scale for the truss drawing is 
usually somewhat smaller than for the details. Great care should 
be exercised in order that connections may be as free from eccen¬ 
tricity and as compact as possible. (12) It is important to so 
space rivets that the net section of any member will not be less 
than was contemplated in the design. (11) When a connec¬ 
tion is too complicated to exactly proportion the rivets, assump¬ 
tions should be made which will be on the safe side. 


Art. 29. 


PROCEDURE FOR PLATE GIRDER BRIDGE. 


65 


29. Order of Procedure for a Plate Girder Bridge. 

The method of procedure for a plate girder bridge may be 
outlined as follows: The scale of the drawing of the girder 
should be % inch, 1 inch or l 1 /^ inch per foot. Two or more 
sheets may be used for long girders. For a skew bridge the full 
length of one girder must be drawn. The girder should be 
drawn first, but it will be necessary to sketch the lateral and 
beam connections before it can be completed. The first thing to 
be considered is the location of the splices in the web. The hand 
books give the maximum lengths obtainable for plates of differ¬ 
ent widths and thicknesses. Web plates up to about 96 inches 
wide may be obtained longer than convenient for handling in 
the shop. Their length should be limited to from 20 to 25 feet., 
except for girders less than 30 feet long whose webs may b^ 
made without a splice. 




The pitch of the rivets in the flanges should be determined 
and regular groups of spacing be decided on, as for example, 
2^4 inch, 2 ]/ 2 inch, 3 inch, 4 y 2 inch and 6 inch. Now the splices 
may be located. If it is a deck girder, they should be so located 
that there will be no odd spaces, if possible, in the groups de¬ 
cided on. Stiffeners are always placed on the splice plates. The 
intermediate stiffeners need not be spaced so exactly equal but 
that they may come on one of the rivets previously located, ex¬ 
cept where the pitch in the flanges is less than 3 inches, in which 
case a space of at least 3 inches will generally be required on 
each side of the stiffener. If the girder is for a through bridge, 
the splices will usually be located at the panel points, from 
which everything else must be located. Through girders often 
have their top flanges bent to a quadrant at the upper corners, 













































66 


PROCEDURE FOR PLATE GIRDER BRIDGE. 


Art. 29. 


and extend down the ends of the girder. This necessitates 
splices in the top flange near the bend so that long pieces will 
not have to be bent. All splices in a flange should break joints. 

In general no countersinking is allowed in girders except in 
the shoe plates. When the rivets in the horizontal leg of a flange 
■angle stagger with those in the vertical leg, some of the former 
will interfere with the outstanding legs of the stiffeners. To 
avoid this, special spacing may be introduced near the stiffener 
or the stiffeners notched as shown in Fig. 26. In unusual cases 
it may also be desirable to notch the other leg of the stiffener 
to clear a rivet. ' 

The horizontal legs of the flange angles are usually as wide 
or wider than the vertical legs. When the vertical leg is 5 inches 
or over, two rows of rivets are used in it. The practice with 
regard to the horizontal leg differs. The simplest way is to have 
also two lines of rivets in each horizontal leg, putting those of 
the inner row in one leg opposite those of the outer row in the 
other leg. This, however, gives more rivets than necessary 
through the flange plates. If only one row of rivets is used in 
each horizontal leg, they should stagger with those in the vertical 
legs. If two rows are used in each leg the spacing in the hori¬ 
zontal legs may be increased to one and one half or two times 
that in the vertical leg. For example, where the spacing in the 
vertical leg is 2% inches, 3 inches and 4:V 2 inches, that in the 
horizontal legs might be 41/2 inches, 4y 2 inches and 6 inches, or 
41,4 inches, 6 inches and 6 inches. When the spacing in one leg 
is 3 inches, for instance, and that in the other is 4 y 2 inches, the 
rivets on the inner row of the 4^ inch spacing will stagger with 
those in the other leg, while those in ifche outer row will come 
opposite. Three lines of rivets are sometimes used in 7 inch 
.and 8 inch legs of angles. 

The minimum.pitch (7) of rivets depends upon the distance 
between rivet lines and the gage of the latter, and is influenced 
by clearance for the riveting tool. In Fig. 27 “g” depends upon 
the thickness of the angle. For large angles, therefore, there 
are usually two standard gages. In crimped stiffeners the dis¬ 
tance “a” Fig. 28 should not be less than 2 inches. Stiffeners 
should be placed with the backs of the angles toward the ends 
of the girder. Flange rivets should not be located closer to 


Art 29. 


PROCEDURE FOR PLATE GIRDER BRIDGE. 


67 



the regular die of the riveting machine. 

Even if fillers are not required under stiffeners, it is best 
to use them at points where beams or frames connect and at the 
splice plates. Connections for beams and frames should, if pos¬ 
sible, be made in such a manner that they may be swung into 
position without striking the rivet heads in the flanges of the 
girders. 

For girder bridges on a grade, the girders should, if pos¬ 
sible, be made so that they will fit if turned end for end. The 
bevel should be in the masonry plates and not in the shoe plates. 




C ) 
( ) 
( ) 


Fig. 29. 


Fig. 28. 


30. Shop Biiis. Shop bills are lists of material for use 
in the shop. They are made on sheets S.fkxll inches or 814x14 
inches. The forms used by different companies differ somewhat, 
but the essential features are as follows: 

They should be numbered consecutively, and should show 
the number of the drawing to which they refer. Each finished 
piece should be billed separately, and the number to be shipped 
should appear in the first column. In the second column should 
be given the number of constituent parts required to make the 
number of members shown in the first column. The main parts 
of members should be given first, the details following, putting 
the lacing last. Shop rivets are not billed. 

The size of each part, the name or location, or both, and its 
length, must be given. Both the finished length and the ordered 
length should be given in separate columns. In the “remarks ’ 7 
column it is usually indicated whether or not a piece is to come 
from the mill or from stock. Blacksmith work, machine work, 
and riveted work are usually put on separate bills. Blank forms 
are sometimes used for pins, bars, field rivets, etc. Be sure that 
nothing is omitted, as it might seriously delay erection. 



























68 


SHOP BILLS. 


Art. 30. 


A check list for various kinds of structures should be pre¬ 
pared, giving all possible items to ship, similar to the 4 ‘Order of 
Estimating” given in Art. 19. By consulting these, omissions 
may be avoided. 

It is usually required to send .drawings to the shop or to 
have them printed for approval, as soon as they are finished. If 
they are sent for approval it may be better and more convenient 
not to make the bills until the prints are returned approved, 
as there may be some changes. Five or six sets of prints are 
required for the shop. Sending out drawings before all parts 
of the structure are drawn up is not the most logical thing to 
do, but is often necessary. 

7 


FOAM No. A 

Sheet No. -277- Cont. No. _ 

THE OHIO STATE BRIDGE COMPANY 

_ Zr/L3$0& __ Dat 


-d./yc/ipe-/7<2J6- -CL hi. szM, _ Drawing No. 74- 


Ship 

No. 

Pcs. 

Kind 

SIZE 

Wt. 

P. Ft. 

DESCRIPTION 

Finished 

Length 

Ordered 

Length 

REMARKS 

4 


r/77. 

77r> CAerr/c. 







4 

sS- 

zs"*? 


Cipy/rr B/ 

2/-9? 

2/-9± 



8 

ll 

3i \3i 4 

8.S 

7op H 

2/-S? 

2/-9s 

s/ 

fp 


fi 

n 


/3. T 

B4. 11 

2/ l 9ta 

£/ : 9£_ 

/f 


8 

s 

/z'-f 


A'4-5 

Z/^fc 

2792 

A> 


8 

s 



A77 . •po/zce 

/-o" 

/Z-0 

ML. ~ 


4 


// 


7/pyyer 

z-r 

/z-o~ 

ML-. ~ 


4 


/S'? 


Brrrtfcf) Bb. 

z-o? 

S4' 

ML. ,, 


fifl 


/* 3" 

2**JT 


LM/4* <* -'- 























Tnfc 

r/77. 

7op Chora 


c. . OO 





2 


ZS - 7 


C & re r B/- 

24-Stz 

’ 

244? 

C&r/7t?a/e 









7 


Fig. 30. 


A simple form of shop bill is shown in Fig. 30. The fol¬ 
lowing information should also be put on a bill sheet and sent 
with the shop bills: 

Contract No. Ship to 

Description Shop Paint 

Location Field Paint 

Date to Ship Lumber furnished by 

Inspected by Penalty 

Erected bv 


l 





































































Art. 31. 


SHIPMENT. 


69 


In general, the drawings should show everything complete, 
but the drawings of the forge work, machine shop work, and 
miscellaneous details are often made on bill sheets. 

31. Shipment. Field splices and connections are often 
determined by the limitations of transportation facilities. These 
should be determined at the outset. Some routes can take care 
of pieces of greater extreme dimensions than others. Tunnels 
often* limit the width of the- loading and overhead bridges, the 
height. Sharp curves have an important bearing on loading 
long pieces, especially girders. It should be remembered that 
a piece extending over two or more cars, swings away from the 
center line of the track on a curve, requiring more clearance 
than on a straight track, and that a car on a curve is inclined 
toward the inside of the curve. Ordinarily, pieces about 10 feet 
high can be transported on the railroads, but the width at the 
top is usually limited to about 6 feet. The greatest width of a 
steel car is 10 feet 2 inches. Pieces 10 feet or more in width 
can be transported if they are not too high or too long. The 
question of weight is not generally an important one, except that 
cars of proper capacity must be used so that no truck will be 
overloaded. It is allowable to put two-thirds of the nominal 
capacity of a car on one truck. 

For export shipment special instruction must be obtained on 
each job as to maximum lengths, weights, etc. Pieces for export 
work must, in some cases, be so small that they can be trans¬ 
ported on pack 'animals. A thorough and simple system of 
marking is necessary. Instead of marks, colors are sometimes 
used. 

The question of cost of freight is sometimes an important 
one, and may determine the maximum length of a piece. If the 
total weight of a contract is less than a car load, so far as cost 
of transportation is concerned, no piece should be longer than 
a car length. 

There are two kinds of freight rotes, ‘‘car load” and less 
than car load” (C. Ij. and L. C. L.), the latter being the higher. 
The minimum car load is generally 30,000 lbs.; the minimum for 
two cars is 40,000 lbs.; and 20,000 lbs. is added for each addi¬ 
tional car. Therefore if any piece extends from one car over 
part of another, freight must be paid on at least 40,000 lbs., no 


70 


MATERIALS. 


Art. 32. 


matter liow much less the shipment weighs. In case of a girder 
extending over three cars, the minimum amount charged would 
be on 60,000 lbs. 

32. Materials. The materials used by the structural en¬ 
gineer are wrought steel, wrought iron, cast steel, cast iron and 
timber. Cast steel and cast iron are used for the machinery of 
draw bridges. Except in special cases of columns for buildings, 
and pedestals, and for small details like washers, ornaments and 
separators, cast iron has passed out of use entirely in structural 
work. Cast steel is sometimes used for shoes of bridges. 

Timber is used for the compression members in combination 
bridges and roof trusses, and for the floors of bridges. 

Wrought Iron is used for rods which must be welded,—rods 
with loop eyes, or forked heads. In the best classes of work welds 
are entirely avoided. Welds in steel are not considered reliable. 

The qualities of the materials required are given in the 
specifications governing the work. We shall consider structural 
steel more in detail. 

At present three kinds of steel are commonly specified, viz., 
‘ ‘ rivet steel,’ ’ “soft steel’ ’ and ‘ ‘medium steel. ’ ’ Of these, rivet 
steel is the softest and medium steel the hardest, or the steel of 
greatest ultimate strength. “Hard steel,” or steel having an 
ultimate strength greater than 70,000 lbs. per sq. in., is seldom 
used for bridges or buildings. 

There is at present a movement toward the adoption of a 
single grade of steel for all structural purposes. 1 This would 
simplify the steel maker’s work, and no doubt result in a more 
uniform and a cheaper product. 

The quality of steel is determined by analysis and test. 
There is considerable uniformity in the requirements of various 
specifications. These may be enumerated as follows: 

Chemical requirements, —Percentage of phosphorus, .sul¬ 
phur, manganese, silicon, carbon, copper and arsenic. . 

Physical requirements, —Process of manufacture, uniform¬ 
ity, finish, heat treatment, ultimate strength, elastic limit, elonga¬ 
tion, reduction of area at point of fracture, appearance of frac- 

’See Bulletin No. 62 American Railway Engineering & Mainte¬ 
nance of Way Association. 



Art. 32. 


MATERIALS. 


71 


ture, bending, bending after quenching, punching, drifting of 
punched holes, variation of cross section and full sized tests. 

Chemical analysis determines the amounts of the impurities 
in steel. All elements except iron and carbon may be called 
impurities. Since it is practically impossible to eliminate all 
the .phosphorus and sulphur, a small percentage of manganese 
is considered advantageous. In order to meet the physical re¬ 
quirements the manufacturer must limit the amount of all 
impurities, and of the carbon. All specifications, however, limit 
the amount of phosphorus allowed, since this element renders 
the steel brittle or “cold short” while it, at the same time, hard¬ 
ens it. Some specifications also specify maximum allowable per¬ 
centages of sulphur, manganese and silicon. The maximum al¬ 
lowable amount of phosphorus in steel depends upon its mode 
of manufacture. It is usually about 0.04% for basic open hearth 
steel and 0.08% for acid open hearth and Bessemer steels. 

Carbon -has the greatest influence upon the ultimate strength 
or hardness of steel. Phosphorus, manganese and sulphur make 
steel harder and also reduce its ductility. 

Basic open hearth steel will, in general, have about the fol¬ 
lowing ultimate strengths, depending upon the percentage of 
ca rbon: 

55000 lbs. per sq. in. with 0.10% carbon. 

60000 lbs. per sq. in. with 0.15% carbon. 

65000 lbs. per sq. in. with 0.20% carbon. 

70000 lbs. per sq. in. with 0.25% carbon. 

The elastic limit will be about 0.6 of the ultimate tensile 
strength. 

There is no rigid line separating the different grades of 
steel, but steel having less than 0.15% carbon is generally soft 
steel, and with more than 0.30% carbon, hard steel, the inter¬ 
mediate grade being medium steel. These grades are usually 
defined by their ultimate strength. 

Process of Manufacture. Steel is made by the Bessemer or 
open hearth process. Open hearth steel is now used for all im¬ 
portant bridge and building work. It is almost invariably re¬ 
quired when a regular specification governs the work. 

Bessemer steel is not so uniform in quality as open hearth 
steel and is, therefore, not so reliable a material. It is made in a 


72 


MATERIALS. 


Art. 32. 


9 


converter, by blowing a blast of air through molten pig iron 
until the carbon and silicon are all burnt out. Ferro-nmnganese 
is then added to recarbonize the metal the required amount and 
to absorb the excess of oxygen, which would make the steel 
“rotten.” From the converter the metal is poured into a ladle 

i 

and then into moulds. Here the metal is allowed to solidify, 
producing ingots. The ingots are reheated and then rolled into 
slabs, blooms and billets of various sizes, depending upon the 
final form into which they are to be rolled. 

Open hearth (Siemens-Martin) steel is made in an open 
hearth furnace and is of two kinds, acid and basic. The use of 
the latter predominates. 

Acid steel is made in a furnace having a lining of a refrac¬ 
tory silicious material which has an acid reaction. Basic steel 
is made in a furnace having a lining of magnesite or dolomite, 
which has a basic reaction. The raw material in either case is 
pig iron, now usually charged in ( a molten state. If the pig iron 
contains larger percentages of phosphorus and sulphur than are 
allowed in the steel, these must be reduced. Since they have a 
great affinity for iron, some reagent must be introduced in the 
molten metal which has a greater affinity for them. For this 
purpose a basic material must be used, since they form acids 
when oxidized. The material employed is lime charged in the 
form of limestone. This cannot be used in an acid lined furnace 
because it would form ,a flux with the lining. In the acid process, 
therefore, the percentages of phosphorus and sulphur in the raw 
material must not much exceed what is allowed in the finished 
product. This process requires a better grade of pig iron than 
the basic process. 

In the open hearth basic process, large quantities of oxide of 
iron in the form of iron ore or mill scale, are charged into the 
furniace, together with limestone and molten pig iron. The lime 
which is formed, combines with part of the phosphorus and 
sulphur, reducing the percentages of these to minute quantities, 
while the oxide of iron serves to burn out the carbon, manganese 
and silicon. The desired amounts of carbon and manganese are 
then added. As in the Bessemer process, the steel is made into 
ingots, billets land slabs, and is finally rolled into the desired 
shapes. 


Art. 32. 


MATERIALS. 


73 


Upon the care with which all of these processes are carried 
out depends the uniformity and finish of the rolled steel, as well 
as its quality to some extent. Lack of uniformity may be due to 
unequal heat treatment, unequal working or to segregation in the 
ingot, producing a steel of variable composition. If a piece of 
steel is not uniformly treated and cooled there may be internal 
stresses in it, hence it is required that pieces which are heated in 
working as eye bars, for example, must be annealed. The hotter 
a piece of steel is heated, the coarser grained it will be and the 
more rapidly it is cooled, the harder it will be. Rolling and ham¬ 
mering steel increases its density and strength, but working it 
at a blue heat may crush the grain, which is very injurious. 
Rough iron cracks are indications of “red shortness” or burning. 
Other surface defects are easily discovered on close inspection. 
Defects due to bad heat treatment, improper working, excess of 
impurities, etc., are discovered by chemical analysis and physical 
tests. Tests are made of material from each heat, melt or blow. 

Specifications allow a range of 8,000 to 10,000 lbs. per sq. 
in. in the ultimate tensile strength of any particular grade of 
steel, but they do not all agree as to the limits. Depending upon 
the specifications, soft steel miay include steel having an ultimate 
strength as low as 52,000 lbs. per sq. in. and as high as 62,000 
lbs. per sq. in., medium steel as low as 60,000 and as high as 
70,000 lbs. per sq. in., and rivet steel from 48,000 to 58,000 lbs. 
per sq. in. 

The ultimate strength, elastic limit, elongation and reduc¬ 
tion of area are determined from test pieces cut from the finished 
material. It is usually required that the elastic limit must not 
be less than one half of the ultimate strength. As it is not diffi¬ 
cult to obtain an elastic.limit equal to 0.6 of the ultimate strength 
it would be well to specify, as is sometimes done, a minimum for 
the elastic limit. Thus, if the ultimia'te may vary from 60,000 to 
68,000 lbs. per sq. in., the minimum elastic limit might be fixed 
at 32,000 lbs., for example, and then steel having a greater ulti¬ 
mate than 64,000 lbs., would have to have an elastic limit of at 
least one half the ultimate. In this case the unit stresses could 
be based upon an elastic limit of 32,000 lbs. 


74 


MATERIALS. 


Art. 32. 


In commercial testing, the elastic limit is determined by the 
drop of the beam of the testing machine, that is, it is really the 
yield point. 1 

It is important that steel be ductile and not brittle. For 
determining ductility, the tension piece is measured after rup¬ 
ture to determine the stretch in an original length of eight 
inches, and the reduction of area at the point of fracture. The 
determination of the latter is not important .and is usually 
omitted. In a general way, the elongation in eight inches is 
about 30% for good steel having an ultimate strength of 56,000 
lbs. per sq. in., and 25% for 65,000 lb. steel. This is for standard 
test specimens having an area of cross section of not less than 
y 2 sq. in. The usual requirements are 25% for soft steel and 
22% for medium. Pin material is only required to have an 
elongation of 16% or 17%, and eye bars, when tested full size, 
10% in the body of the bar. 


The percentage of reduction of area is about 1.8 to 1.9 times 
that of the elongation. 

The appearance of the surface of the fracture is always 
noted in testing steel. If it shows defects such as blisters, cin¬ 
ders, spots, cracks or lack of uniformity of color, it is not a 
desirable product. The fracture of good material is described 
as “silky,'’ and has a “uniform, fine grained, structure of blue 
steel gray color, ’entirely free from fiery ‘luster’ or a ‘blackish' 
cast,” If the fracture is granular and has a ‘fiery” lutser it 
indicates over heating. If the fracture is dull or “sandy,” the 
steel is impure, or worked cold, and should be rejected. 


The bending test requires that the test piece shall bend cold 
without sign of fracture. For soft steel it must bend flat on 
itself, and for medium steel, to a curve whose diameter is from 
one to three times the thickness of the piece tested. Some speci¬ 
fications require this bending test to be made upon pieces which 
have been heated and quenched in water. 


A punching test is sometimes specified. This requires that 
the walls between the punched holes shall not break down except 
when they are less than % inch thick. 


] See Heller’s “Stresses in Structures,” Art. 21. 



Art. 33. 


INSPECTION. 


75 


The drifting test requires that the ductility of the metal 
must be such that a punched hole will stand drifting until its 
diameter is increased from 33% to 100% without cracking the 
edges. 

Pieces of large cross section are apt to be “piped/’ that 
is, they are not solid. This is due to bad working or unequal 
cooling, and occurs particularly in pins. It is usually specified 
that the larger sizes of pins (say over 4% inches) must be forged 
from blooms having a sectional area of about three times the 
area of the pin, in order that the material may be sufficiently 
worked to make it sound. 

Full sized tests are usually confined to eye bars. Some re¬ 
ductions in requirements of ultimate strength and elongation 
are made from those required for small test pieces, because 
pieces of large cross section do not test as high as those of small 
cross section. 

33. Inspection. If an inspector is employed on a con¬ 
tract, his duties may relate to material, shop work and erection. 
On some classes of work the purchaser employs no inspector. 
The manufacturer has all work inspected as to dimensions, to 
avoid trouble in erection. In some cases reports of tests of 
material are furnished by the rolling mill, which conducts a test¬ 
ing department for this and other purposes. 

An inspector is most frequently employed to make tests of 
the steel, at* the mill, as it is rolled. The shop work is also 
inspected for the best classes of work, but in comparatively few 
cases is the field work inspected by a regular inspector. The 
large railway companies have inspectors in the mills, the shop, 
and the field. 

The inspection of material includes tests, analyses, surface 
inspection, measuring sizes, etc., of steel, lumber, paint, etc. A 
shop inspector should see that no material is injuriously treated, 
that reaming of rivet holes is properly done, that all parts are 
made in accordance with the drawings, that rivets are good and 
tight, that members are straight, that no work is ragged or un¬ 
finished, that painting is done in accordance with the specifica¬ 
tions, and should make reports of progress. 


76 


INSPECTION. 


Art. 33. 


The field inspector should see that no part of the structure 
is injuriously treated, that no members are interchanged, that all 
field driven rivets are good, and that the painting is properly 
done. 

Rare qualifications are required for a good inspector. He 
must serve his employer honestly and avoid friction with the 
contractor. 


CHAPTER IV. 


ROOFS. 

The roofs of buildings in which it is not desirable to have 
columns at frequent intervals, are supported by means of trusses 
which are in turn carried either on columns at the sides or on 
masonry walls. These trusses may be either of steel or a com¬ 
bination of wood and steel. Steel trusses are usually used in 
steel or brick, mill and factory buildings, and in fire proof 
buildings. Combination trusses are used in wooden buildings 
requiring a large floor space free from columns, and often also 
in large brick and stone buildings, such as churches and public 
buildings of all kinds. 

34. Construction. The roof trusses are placed trans¬ 
versely of the building, their distance apart (See Art. 37) de¬ 
pending on the length of span, type of construction of the 
building in general and the kind of roof covering. The upper 
inclined members of the trusses, parallel to the slope of the roof 
are called rafters. (See Fig. 31.) Longitudinal beams extend¬ 
ing from truss to truss are supported by the trusses at intervals 
along the rafters. These are purlins, and they carry the roof 
covering, either directly or by means of boards, called sheeting 
or sheathing, running transversely to the purlins (up and down 
the roof) or diagonally across them. 

35. Roof Coverings. For mill buildings, the commonest 
kinds of roofing are corrugated steel or iron, slate, tile, tin and 
various patent sheet metal roofs, tar and gravel and similar 
patented combinations. 

The corrugated steel or iron is usually fastened directly to 
the purlins by means of clips. 1 Slate is usually nailed to sheet- 
in o* boards with a. laver of roofing felt between, although some- 
times heavy slate is fastened directly to small purlins placed 
about 10y 2 inches apart. Tile is usually fastened directly to 

] See “General Specifications for Steel Roofs and Buildings,” by 
C. E. Fowler, Figures page 17. 




78 


TYPES O* TRUSSES. 


Art. 3G. 


angle purlins spaced about 13 inches apart, without any sheet¬ 
ing. Tin, and similar types of roofing are laid on sheeting with 
roofing felt between. Tar and gravel roofs are laid on wooder 
sheeting or sometimes on reinforced concrete slabs. 

The main function of the roof is to shed water, and in order 
to do this without leakage, it must have a fall or slope. The 
amount of slope required depends upon the kind of roof 
covering. 

The pitch of a roof is the ratio of its rise to its' span. Thus 
for a 60 ft. span, if the rise is 15 ft., the pitch is if the rise 
is 20 ft. the pitch is %. The least pitch advisable to use with 
corrugated steel slate or tile is about 14 , that is a fall of about 
6 inches per foot, and this is the pitch used for most mill and 
factory buildings. Tin and similar roofs with water tight joints 
may have a fall of as little as % inch per foot. Tar and gravel 
roofs should have a fall of from % in. to 2 in. per foot. 

36. Types of Trusses. It is only in unusual structures 
such as train sheds, exposition buildings, grand stands, etc., 
that the span of a roof truss exceeds 100 ft. The slope of the 
roof and local conditions such as required clearances, ventila¬ 
tion, light, etc., will usually determine the general outline of the 
truss. Any type of bracing may then be selected to suit the 
materials of construction. 1 

For roofs of ordinary pitch and span, the Fink truss is by 
far the commonest type. Figure 31 (a), (b), (c) and (d) shows 
several modifications of this form of truss, to suit spans of vary¬ 
ing length. For sake of economy in the rafters it is not desirable 
to have many loads coming on them from the roof purlins, be¬ 
tween panel points, hence the advisability of increasing the 
number*of panels as the span increases. 

For combination trusses of wood and iron, one of the forms 
shown in Fig. 31 (g) and (h) is used. In these trusses the 
diagonal compression members and the top and bottom chords 
are made of wood, and the vertical ties are rods. 

For flat roofs some form of truss must be used similar to 
Fig. 31 (f), (h) and (1), in order to gain sufficient depth at the 
center to gave economic chord sections. 

J See Heller’s “Stresses in Structures,” Art. 117. 

See Ketchum’s “Steel Mill Buildings,” page 14G. 



Art. 36. 


TYPES OF TRUSSES. 


71) 


Another type of roof which is rapidly coming into favor is 
the saw-tooth”, roof, shown in Fig. 31 (k). The plane of the 
steeper rafter is glazed, and this side is made to face the North 
if* possible. "By this arrangement the floor below is lighted by 
an even diffused light, without the necessity of making the 
building narrow in order to gain light from the sides, and with¬ 
out the disadvantages of sky lights through which the direct 
rays of the sun may shine. 

Roof trusses for very long spans are usually three-hinged 
arches, the lower hinges being connected by bars under the floor 
to take the thrust. 1 


(a) Fink Trusses. (b) 



(e) FTruF Trusses if) 



(A) (/) 

J5u/r7oo//7 /?oof Tr/nn^n/ur 7russ 

Fig. 31. 


The roof trusses of grandstands usually project beyond 
their supports at both ends. These are called cantilever trusses. 

Sometimes for the sake of appearance or to gain clearance, 
the lower chord of a roof truss is curved upward. This always 
increases the cost and weight very materially. 


*See trainsheds for Penna. R. R. at Jersey City and Philadelphia, 
and of the Phila. and Reading R. R. at Philadelphia, in Eng. News, Vol. 
26, p. 276 and Vol. 29, pp. 507 and 508, Vol. 42, p. 212. 















































80 


BUILDING CONSTRUCTION. 


Art. 37. 


Ordinary roof trusses are made with riveted connections, 
because such construction is cheaper and gives greater rigidity 
than the pin connection. Heavy trusses of long span are some¬ 
times made with pin connections, because the saving in cost of 
erection is more than the saving in shop work with riveted con¬ 
nections. The members of a pin connected truss offer a smaller 
percentage of area to the corrosive action of gases than those 
of riveted trusses. Provision is sometimes made for the weaken¬ 
ing effect of corrosion, by increasing the thickness of material 
above that required to take the actual stresses or by adding a 
certain percentage to the loads. 1 

In calculating the relative economy of roofs of different 
pitches, the roof covering must be taken into account, as the 
greater the pitch, the greater the area of roof covering. Corru¬ 
gated steel usually makes the cheapest roof, as the dead weight 
is small. The most expensive roofs are those of tile and heavy 
slate, laid directly on the purlins. 

37. Building Construction. Trusses carrying light roofs 
are usually spaced from 16 ft. to 20 ft. center to center. Theo¬ 
retically the shorter this spacing, the less the total weight of 
trusses and purlins, per sq. ft. of covered area, but on account 
•of practical limitations in the size of materials, etc., 2 and on 
account of the greater cost per pound for the manufacture of 
trusses, than for purlins, the spacing of the heaviest trusses is 
very seldom less than 10 ft. center to center. When the weight 
of the roof covering is very great, the purlins are sometimes 
supported between trusses, on beams called “jack rafters 
Which are supported at the ridge and eave, on longitudinal 
beams, carried by the trusses. 

For a building with masonry walls, no wind bracing is 
necessary unless the end walls do not run up to the roof, but 
some bracing is usually put in to facilitate erection and to 
stiffen the roof. 

In steel buildings bracing is necessary to provide for both 
longitudinal and transverse wind forces, and to stiffen the build¬ 
ing in case there is any vibration due to live loads, shafting or 

machinerv. 

%/ 

1! See Fowler’s Specifications for Steel Roofs and Buildings, Art. 10. 

2 See Fowler’s Spec. Arts. 37, 39, 44, 45, 59, and 64. 



Art. 37. 


BUILDING CONSTRUCTION. 


81 


With the ordinary Fink truss, the transverse bracing: con- 



columns run through to the 
Longitudinal bracing may 
in the plane of the rafters is 
plane of the bottom chords is 


sists of knee braces connecting 
the trusses and columns, as 
shown in Fig. 32, the wind load 
being carried to the founda¬ 
tions by bending in the columns. 
If a truss is used having some 
depth at the ends, (see Fig. 31 
(f), (h), (1),) the knee braces 
may be dispensed with and the 
rafter. 1 

be put in, in three planes. That 
called rafter bracing, that in the 
called bottom chord bracing , and 


that in the vertical planes between the columns is called side 
bracing. 

Theoretically, only one panel of longitudinal bracing is 
necessary to take care of the longitudinal wind forces, but for 
convenience in erecting the steel work, not less than two panels 
are braced, and in long buildings the braced panels are not 
farther apart than three or four panels. This arrangement us¬ 
ually requires less material in the bottom chord and rafter 
bracing diagonals than is given by the smallest size of rod ever 
used, and these members are therefore usually made of % inch 
round rods. Struts are required between the trusses and col¬ 
umns as members of the lateral systems. In the rafter bracing, 
the roof purlins are usually made to serve the purpose of struts. 
Several lines of ties are put between the bottom chords of the 
trusses in the unbraced panels. These serve to reduce the vibra¬ 
tion of the roof, especially when cranes or hoists are attached to 
the trusses. The general arrangement of the bracing is shown 
in the stress sheet, Fig. 35. 

38. Loads. A roof truss ordinarily carries nothing but 
dead loads, which includes wind and snow loads and the weight 
of the structure itself, such as the covering, sheeting, purlins, 
trusses, bracing, ceiling, shafting, etc. A traveling hoist carried 


by a roof truss would constitute a live load. 


a For figuring stresses in Columns see Heller’s “Stresses in Struc¬ 
tures,” Chap. X and XIII. 











82 


LOADS. 


Art. 38. 


The pressure of a gas or liquid is always normal to the 
surface on which it acts, consequently the wind load acts nor¬ 
mally to the surface of the roof. All other loads act vertically, 
and are estimated in pounds per horizontal square foot. The 
wind is assumed to blow horizontally, the pressure which it 
exerts depending* upon its velocity. An empirical formula fre¬ 
quently used is 17=0.0047 2 in which 17 is pressure per sq. ft. 
in pounds, on a surface perpendicular to the direction of the 
wind, and V is velocity in miles per hour. Experiments extend¬ 
ing* over seven years at the site of the Forth bridge in Scotland, 
show that the pressure on large surfaces is much less per sq. ft. 
than on small ones. The maximum pressure recorded on a 
surface of 1 y 2 sq. ft., was 41 lbs, per sq. ft., and on a surface 
of 300 sq. ft., was only 27 lbs. per sq. ft. 

The roof of a building presents a large surface, and is 
usually figured for a wind load due to a horizontal force of 30 
lbs. per sq. ft. The sides and ends of buildings are usually 
figured for a. maximum wind pressure of from 20 to 30 lbs. per 
sq. ft., but this pressure is often taken as low as 10 lbs. per 
sq. ft. 1 

The normal wind pressures on roofs of various pitches for 
a horizontal wind force of 30 lbs. per sq. ft. are given in Fow¬ 
ler’s Specifications for Steel Koofs and Buildihgs, Art. 6. These 
are based on the empirical formula, 

W / =Wsin^ 1 - s4Cosa ~ 1) in which 

I7'=normal pressure per sq. ft. 

17 =horizontal pressure per sq. ft, 

a =angle of inclination of the roof with the horizontal. 

In the article referred to, the columns marked “Vertical” 
and “ Horizontal” are not the ordinary components of the nor¬ 
mal given, but they do not differ much from them. 

When a roof truss rests on masonry walls, one end must be 
free to move longitudinally, in order to provide for changes in 
length due to temperature changes. This is usually arranged 
by providing slotted holes in one end for the anchor bolts, thus 
allowing the truss to slide on the bed plate. For long trusses 
rollers are provided to reduce the friction where this movement 


J See Fowler’s Specifications, Art. 7. 




Art. 38. 


LOADS. 


83 


takes place. If we assume that there is no friction at the ex¬ 
pansion bearing, the reaction must be vertical at that point and 
therefore it is necessary to calculate the stresses in the truss 
with the wind blowing from both directions. When trusses are 
fastened rigidly to the top of columns, the horizontal compo¬ 
nents of the wind reactions are sometimes assumed to be equal 
and sometimes the wind reactions are assumed parallel. In the 
latter case it is only necessary to calculate the stresses for the 
wind blowing in one direction. A vertical equivalent wind load 
is sometimes used together with the other loads, as explained 
below. 

The snow load varies with the climate, the slope of the roof 
and the roughness of the roof covering. 1 The weight of freshly 
fallen snow is from 5 to 12 pounds per cu. ft. 2 The snow load 
may act on one side only of i a roof, as a heavy wind or the sun 
on the other side would dislodge it. When the pitch of the roof 
is variable, as it frequently is for train sheds, snow might stand 
on only a part of either or both sides, and might be a variable 
load. It is not usually assumed that the maximum wind and 
snow loads can act upon one side of a roof at the same time, 
because the wind would dislodge the snow. 

We may therefore have a partial snow load, a partial wind 
load or a combination of these, in addition to the weight of the 
structure itself. 

For the ordinary Fink roof truss of % pitch or less, none of 
these partial loads give maximum stresses, and an equivalent 
wind and snow load is usually taken as acting vertically over 
the entire roof. This simplifies the calculation of stresses, and 
is used whether or not the trusses rest on rollers at one end. 3 

The weight of the roof covering should be calculated, re¬ 
membering that the weight per horizontal square foot is equal 
to the weight per sq. ft. of the roof surface multiplied by the 
secant of the angle of inclination of the roof with the hori¬ 
zontal. 4 


] See Fowler’s Specifications, Art. 5. 

2 See Trautwine’s “Civil Engineer’s Pocket Book,” p. 384. 

3 See Fowler’s Specifications, Art. 12. 

4For weights of various roofing materials, see Trautwine’s “Civil 
Engineer’s Pocket Book.” See also Fowler’s Specifications. Art. 8. 



84 


LOADS. 


Art. 38. 


The thickness of the sheeting when used depends upon the 
spacing of the purlins. It varies from % in. to 2 in. in thick¬ 
ness, and may be calculated, using an extreme fiber stress of 
from 1200 to 1500 lbs. per sq. in. 1 2 

The weight of the purlins may be calculated after they are 
designed, which is usually done before the trusses are figured. 
For corrugated iron roofs they will usually amount to about 
3 lbs. per horizontal square foot. 

The weight of the trusses may be estimated from a compari¬ 
son with a similar building which has been designed, or it 
may be approximately obtained from an empirical formula.- 
After the design is completed, an estimate of the weight is made 
and the dead load used in the calculations is verified. If this 

differs materially from the amount used, corrections in the 

# 

design should be made. 

39. Stresses. The stresses in any statically determinate 
structure 3 may be calculated from the principles of statics. 4 For 
ordinary trusses the loads and reactions are all taken vertical. 
Since trusses of the same type with the same number of panels 
are similar figures, the stresses in them are proportional, for 
different spans, to the panel loads. Tables of stresses in various 
types of trusses for panel loads of one pound are given in var¬ 
ious hand books. 5 The stress in any member of a truss similar 
to any of these is gotten by multiplying the coefficient given, by 
the panel load. This is readily done on the slide rule. 

40. The Design of a Roof. To illustrate the method of 
procedure we will now give a complete design of a roof. The 
following data will be assumed: 

The extreme width out to out of pilasters will be 81 ft. 1 in. 

The extreme length of building will be 221 ft. 1 in. This 
will give a length of 220 ft. center to center of end walls, as¬ 
suming the walls to be 13 in. thick, and a width of 80 ft. center 
to center. 


4 See Fowler’s Specifictions, Art. 22. 

2 See Fowler’s Specifications, Art. 9. 

3 See Heller’s “Stresses in Structures,” Art. 42. 

4 See Heller’s “Stresses in Structures,” Chapters III, IV, V and VI. 

5 See Fowler’s Specifications, pages 10 to 15. See also Carnegie’s 
Pocketbook, page 174. 



Art. 40. 


THE DESIGN OF A ROOF. 


85 


The end walls will run up to the roof and carry the end 
panel purlins. 

We will use 11 bays at 20 ft.—220 ft. 

Roof covering to be No. 20 Corrugated Steel. 

Specifications to be Fowler’s “Specifications for' Steel Roofs 
and Buildings,” 1904 edition. 

Pitch of the roof to be one fourth. 

The stress sheet, Fig. 35, gives a general outline of the 
arrangement of the purlins, bracing, etc. 

The student should familiarize himself with the specifica¬ 
tions and refer to them constantly. 

Loads:—Snow (Spec. Art. 5) 15 lbs. per horiz. sq. ft. 

Wind (Spec. Art. 6 ) Vertical 15 lbs. per horiz. sq. ft. 

Corr. Steel No. 20 (Spec. Art. 8 ) 2 lbs. per horiz. sq. ft. 

Purlins say 3 lbs. per horiz. sq. ft. 

Total carried by the Purlins 35 lbs. per horiz. sq. ft. 

For corrugated steel No. 20 the roof purlins must not be 
spaced over 4 ft. 6 in. center to center (Spec. Art. 27). The 

extreme length of the rafter is 7 / (40.5) 2 4-(20.25)-=45.3 ft. If 
we use 11 purlins, their distance center to center will be almost 
exactly 4 ft. 6 in. This arrangement will not make the purlins 
come 'at the panel points of the truss (See Fig. 35) but this can¬ 
not be avoided, hence the rafters must also act as beams to carry 
the purlin loads to the- panel points of the truss, as Avell as 
members taking the regular truss stress. 

The number of horizontal square feet tributary to each 
81 

purlin is —X 20=81 sq. ft., which at 35 lbs. per sq. ft. gives 
20 

2835 lbs. total load on each purlin. The maximum moment 

_WL^ __ 2835X20 _ y pgg £ 7 . lbs.=85,050 in. lbs. The maxi- 
8 8 

mum allowed extreme fiber stress for purlins is 15000 lbs. per 
sq. in. (Spec. Art. 19). 

— = — — 5.67=required section modulus. 

s v 15000 

The lightest I beam with a section modulus greater than 
5.67, is a 6 in. I x 1214 lbs. (See Cambria, page 160). The light¬ 
est channel having the required section modulus in a 7 in. chan- 










86 


THE DESIGN OF A ROOF. 


Art, 40. 


nel 9% lbs., the lightest angle that can be used is a 7 in. x 3% in* 
x y 2 in., which weighs 17.0 lbs. per ft. The I beam would be 
better than the channel, because it is considerably stiffer side- 
wise, but it weighs considerably more. Channels are usually 
used in such positions and we will use the channel. 

The above method of calculating purlins is not correct, 
since the moment of inertia which we used in the calculation is 
not about 'an axis perpendicular to the plane of the loads. 1 It 
is, however, close enough if the purlins are held from deflecting 
in the plane of the roof, and is the method always used. To pre¬ 
vent the purlins from sagging and to take the component of the 
load parallel to the roof, sag ties are inserted at distances not 
more than about 30 times the width of the purlin apart. (Spec. 
Art. 42.) These are usually made of % in. round rods threaded 
at the ends, which are run through holes in the purlin webs with 
nuts to hold them in place. They are carried across the ridge 
in such a manner that the loads on the two sides of the roof 
balance each other. 

The purlins are fastened to the rafters by means of angle 
clips as shown in the truss drawing, Fig. 36 (Spec. Art. 49). 
The clip should be below the purlin to facilitate erection. 

We can now make an estimate of the weight of our purlins. 

One purlin weighs 9% X 20=195 lbs. 22 purlins=22X195 
=4290 lbs. per bay. Sag ties=3X2X46=276 lin. ft. 276X104 
=287 lbs. per bay. About 10% should be added to this for nuts 
and laps, making 320 lbs. per bay. Total weight then is 
320+4290=4610 lbs. per bay. This is distributed over 81X20 

=1620 sq. ft. The weight per sq. ft. then is -^^=2.85 lbs. per 

1620 1 

sq. ft. Our estimate was 3 lbs. per sq. ft. 

The weight of the trusses may now be calculated approxi¬ 
mately from the formula given in Art. 9 of the specifications. 
0.04X80+0.4=3.6 lbs. per sq. ft. Calling this 4 lbs. we have 
35+4=39 lbs. per horiz. sq. ft. for the truss load. For the 
purlin spacing which we have, no two panel loads on the truss 
will, in general, be the same, but it is sufficiently close to assume 


*For a complete discussion of this subject see Heller’s “Stresses 
in Structures,” Art. 69. 







Art. 40. 


THE DESIGN OF A ROOF. 


87 


them all equal for the stresses in the truss. The panel load then 
will be 10X20X39=7800 lbs. 


By means of the table on page 13 of the specifications, we 
find the following stresses for a panel load of 7800 lbs. (Note 
that the lettering of the truss in the specifications is not the 
same as used here.) 


£ 


Mem. 

Stress 

/7/Joh'ec/ 

77/7,7 

ffeq-. 

77rea 

Ma/er/a/ asec/ 

Fact. 

Gi/r. 

Lenyi 

T/c/na/ 

' 77rea 

crB 

BC 

CD 

DE 

+ 6//OO 
+ 67,600 
+54,100 
+50.600 . 

| /5ooo 


Benc/inq 1 „ „ _ 

a no/D/recf l 2 b 6 *33 */> ~]P 

5tress I 

ccmh/net/j 

~zr 

7/3 

773 

77.3 

773 


ab 

be 

ce 

-54,600 

-46.600 

-3/200 

75,000 

99 

364 

3.12 
2M 

2b 3i'*3£ M 1§' &77iy. Jt_ 

00 ****** 0* Ar 09 

2 b 3* 23"$' ~ ~ . 



3.7/770 
// // 

2.27 " 

Sb 

Cc 

A/ 

7,000 
+74,000 
+ 7,000 

Zooo 

6,550 

7,900 

089 

2/4 

0A9 

2 b 2 *2'"$- 

2 b 3 ~ 2/7*$ ir 

2 b2*2*$ nr 

0.6/ 

035 

0.6/ 

56 

773 

5.6 

7.66 

2.64 

7.86 

bC 

Cc/ 

cc/ 

c/E 

Ee 

- 7,600 
~ 7,600 
-75,600 
-23,400 
O 

75,000 

97 

97 

99 

0.52 

O.S2 

7.04 

756 

2 b 2 *2 *3 "§77iv. JL 

0 00 00 00 % 00 00 ♦ 

ZI±2i'-ZH~ - - JL 
*0 00 0*0 00 00 00 

2 b z"*2 *3 

• 


7.50fe1 

00 00 

7.76 * 

00 *0 



Fig. 33. 


The tension members may be proportioned first. The small¬ 
est t^igle allowed is 2 in. X 2 in. X % in-, (Spec. Art. 64), and 
all members should be symmetrical (Spec. Art. 39 and 40). 
Therefore the smallest member allowed will be 2 Ls 2"X2"X 1 /4 // - 
The largest rivets allowed in these angles are % in. (See Cam¬ 
bria, page 54). The gross area is 2X0.94=1.88 sq. in. The net 
area is 1.88— (2X 1 /4X (%+%) =4-88—0.38=1.50 sq. in. This 
will answer for bC, Cd and cd , but cd and dE are usually 
made continuous and should therefore be the some size. 
2 Ls 2 1 /o' / X 2 "X 1 / 4 / / will answer for these, the net area being 
2X1-07— 2X 1 AX (%+%)— 1-76 sq. in. For light trusses ab 
and be are also usually made continuous. The sizes of the other 
tension members are easily determined, as shown in the table 
above. 




















88 


THE DESIGN OF A ROOF. 


Art, 40. 


We will try to make each of tlie compression members of two 
angles. These will be back to back, and will be far enough 
apart to admit the connection or gusset plates between them at 
the joints. We will try to make all gusset plates % in. thick. The 
radius of gyration for the various sizes of angles may be taken 
from Cambria, pages 189 to 193. The least width of compression 

member allowed is of the length (Spec. Art. 59), therefore 

2"X2 "Ls cannot be used in compression members whose length 
is greater than 100 in.=8.3 ft. For Bb and Dd we will try 
2 Ls 2' / X2' / X 1 / 4 // . The least radius of gyration is 0.61. The 

maximum allowed units tress is 12500—500- - 1 - =7900 lbs. per 

0.61 

so. in. • The required area will be -^^=0.89 sci. in., while the 
1 7900 ’ 

actual area is 1.88 sq. in., and therefore Bb and Dd may be 

made of 2 Ls 2 ,/ X 2 ,, X 1 / / 4 ' / . 

For Cc the least allowable width of member will be 


11.3X12 

50 


—2.71 in.' 


The least angles that can be used will be 


2 Ls 3 / 'X2V 2 "XW / unless “special” angles are used, which us¬ 
ually take longer for delivery from the mills and might thus 
delay the work. The table of column unit stresses on page 15 
of the specifications may be used instead of applying the column 
formula each time. Trying 2 Ls 3"X2V2 // X 1 /4 // f°r Cc, the least 


radius of gyration=0.95 and — = —— 

r 0.95 

stress from table=6,550 lbs. per sq. in. 


= 11.9. Allowed unit 
The required area- 


14000 

6550 


= 2.14 sq. 


in. 


The actual area=2X 1.32=2.64 sq. in 


which is sufficient. 


The rafter should be made continuous from eave to ridge, 
if this length is not too great, say over 60 ft. It must be pro¬ 
portioned for direct compression and bending. 1 The maximum 
compression occurs in aB, and the bending in this case is also 
a maximum in this panel, or nearly so. aB is loaded trans¬ 
versely by the purlins, as shown in Fig. 34. Considering the 


x For a complete discussion of this subject see Heller’s “Stresses 
in Structures,” Art. 111. 







Art. 40. 


THE DESIGN OF A ROOF. 


89 


member as a simple beam supported at a and B, the maximum 
moment will be 2509X3.55=8907 ft. lbs. 


The rafter is not really in the condition of a beam simply 
supported at the ends, nor are the ends fixed, because the con¬ 
nections are elastic. The 
actual moment lies some¬ 
where between that for 
the two conditions of free 
and fixed ends, (Spec. Art. 
16) and may safely be 
taken as % of the moment 
for a simple beam. We 
have then ili=%X8907= 
5567 ft. lbs.=66800 in. lbs. 
This is the positive moment under the load nearest the middle. 
There is also a negative moment at each support which may be 
assumed to be equal to the same amount, consequently in apply¬ 
ing the formula of Art. 16 of the Spec., the factor n must be 
taken as the greatest distance from the neutral axis to the 
extreme fiber. 



s= — n 4 - -- We will try 2 Ls 6"X3%"X%". 1=2X16.59 

/ A 


=33.18. 


n- 


1.92. 


A=2X 4.5=9.0. 


66800X8.92 
38.18 


-4 


61100 

9.0 


=7891-j-6789=14680 lbs. per sq. in. The allowed fiber stress 
is 15000 lbs. per sq. in., therefore these angles are large enough. 
If the next size smaller angle be tried it will be found too small. 

The laterial struts do not carry much stress, and their size 
is determined by Art. 59 of the specifications, which requires 

that their least width be not less than - 5 J o of their length. This 


requires the use of members not less than 1.8 in. wide. The 
most economical section will be 2 Ls 5"X3"X iV', the longer legs 

being back to back. The ridge strut is usually made the same 
for all bays. The bottom chord ties take no definite stress, but 

should not be less than one angle 3% ,, X3"X i%" with the 3% 

inch leg vertical. All the laterals may be % in. round rods. 
The vertical member of the truss at the middle takes no stress, 
but keeps the lower chord from sagging. 













81-r Out to Out. 



\ 

£ 

1 

v ^ 


csi 


&> 


V s Qj W . fv 


^i. • ift js 

^J'S l> 

4! ^ d 

O— ^ (V V! M 

•k | ^ 


»| 


§ 

I 


Q> 

J 

"Q 


=g^<3^-£ 

Ct ^ 


’I'O 
Q 

R 



Fig. 35. 




































































































































Art. 41. 


THE DETAIL DRAWINGS. 


91 


41. The Detail Drawings. (27) Having completed the 
designing of the members, what is known as the stress sheet (21) 
is usually next made. This is ordinarily a line diagram as shown 
in Fig. 35, on which are written the stresses and sizes of all the 
members, as well as the general dimensions. After this is com¬ 
pleted the shop drawings may be commenced. 

To avoid eccentric stresses the center of gravity lines of all 
members coming together at a joint should intersect in one 
point. This is not practical in roof trusses because the drawings 
and templet work would be too complicated. Instead of using 
the gravity lines as center lines, the rivet gage lines are used. 
For members composed of 2 Ls 2"X2' / X 1 /4 // the gravity line is 
0.59 in. from the backs of the angles, while the rivet line is 
iy 8 in. out. This makes the eccentricity of the connection 0.535 
in. For a member composed of two angles 3 1 /2 ,/ X3 : (/2 // X tV' 
the eccentricity is 2.00—0.99=1.01 in. For an angle having- 
two gage lines, the center should of course be taken on that rivet 
line which is nearest the gravity line. For a. member composed 
of 2 Ls 6 // X3 1 /2 // XW / the center of gravity is 2.08 in. from the 
back of the shorter leg. The rivet lines in a 6 inch leg may be 
spaced 2 in. and 4 y 2 in. from the back of the angle, and of course 
the inside gage line should be used as the center line. 

In a roof truss it is the practice to have the center lines 
intersect in a single point at each joint except the shoe, joint a, 
Fig. 36. In order to take the reaction, the truss must have an 
appreciable depth at the end, consequently the center lines of 
the rafter and bottom chord are made to intersect at some little 
distance beyond the center of the bearing plate, as shown in 
Fig. 36. To facilitate the driving of the rivets, the depth at the 
end should be at least 6 inches. The distance from the center of 
bearing to the intersection is usually made such an amount as 
will avoid odd fractions of an inch in the center lengths. 

Having determined this point by scale, the slope of the 
center line of the rafter is made exactly 6 in. vertical to 12 in. 
horizontal, for a V± pitch roof. 

The usual standard size of shop drawings is 24"X36". The 
border line should be a single heavy line placed *4 inch from 
the line on which the tracing is trimmed. (Or see Fig. 25.) 


92 


THE DETAIL DRAWINGS. 


Art. 41. 


The truss outline and the details are not drawn to the same 
seale. This amounts to drawing the detail of each joint separ¬ 
ately and then assembling the joints into the form of a truss. 
It is not necessary to show the members broken between joints, 
although the distances are not to scale. Any rivet spacing 
between panel points cannot be drawn to scale, but it is not 
necessary to show all the rivets if the figures locating them are 
properly given. The scale for details is usually 1 in. or iy 2 in. 
per ft., depending upon the available room. The larger scale 
is easier to work with, especially for the beginner. The scale 
for the center lines should be so selected that there will be 
sufficient room for the elevation of half the truss, the dimension 
lines, the top view of the rafter and the sectional view T of the 
bottom chord, with all connections for purlins, laterals, etc. The 
scale for the details must be decided upon first. A sample 
drawing should be consulted and studied, and if necessary pre¬ 
liminary sketches made of the lateral connections. Compact¬ 
ness is desirable, but crowding, especially of dimension lines, 

should be avoided. Usuallv the scale for the outline should not 

* 

be less than one half that of the details. 

Usually on the same sheet with the truss there is put a dia¬ 
gram of the roof showing the location of trusses, bracing, etc., 
similar to Fig. 35. This is called an erection diagram. In a 
building with steel columns and other steel work, the erection 
diagram usually occupies a sheet by itself. Sometimes there is 
also sufficient room on the sheet with the truss drawing for 
drawings of struts, purlins, etc. 

After the scales have been determined, one half the dis¬ 
tance between the interactions of the center lines of the rafters 
and bottom chord (40'—1(%" in our case) is laid off horizon¬ 
tally to the smaller scale chosen for the outline, and one half 
of this distance, if the roof has % pitch, (20'—b 1 ^") is laid 
off vertically at the right end, this being the rise of the center 
line of the rafter above the bottom chord. Now the hypotenuse 
of the right triangle is drawn, which is the center line of the 
rafter. This center line is then divided into four equal spaces, 
and the center lines of the members Bb, Cc and Dd are drawn 
perpendicular to it. The intersections of Bb and Cc with the 
bottom chord determine points b and c , and of Dd with cE, point 


Art. 41. 


THE DETAIL DRAWINGS. 


93 


d. The length of Cc is twice that of Bb and Dd, and equals aB. 
The lengths of ab, be, bC, Cd, cd and dE are equal. Thus it is 
seen that the center lengths are very easily determined, as given 
in Fig. 36, from right triangles. 

Joint a . Fig. 36 is a shop drawing of the truss. The forces 
acting at joint a are the rafter stress, the bottom chord stress, 
the purlin load and the reaction. There must be enough rivets 
in the joint to safely transmit these forces. To avoid changing 
punches, (6) the rivets will be made % in. throughout. (Maxi¬ 
mum size for a 2 in. leg.) Joint a has larger stresses than any 
other, and if % in. connection plates were used throughout it 
would result in a large gusset here, consequently, (5) w r e will 
use a I/O in* gusset plate at a and make all the others % in. 

The rafter stress is 61,100 lbs. The value of a % in. rivet 
in double shear is 6136 lbs. (This value is less than the bearing 
value on a % in. plate). The number of rivets required in the 

rafter connection^ 61 — =10 rivets. We will have to add an 

6186 

extra rivet to transfer the purlin load, this makes 11 rivets. The 
rivets immediately over the bearing plate in the bottom chord 
must transfer the vertical component of the rafter stress and 
the purlin load to the bottom chord angles which rest on the 
bearing plate. 

The amount of this reaction will be 4X7800=31200 lbs., 

31200 

and the number of rivets required =- = 6. In addition to 

6136 

these we must have in the bottom chord sufficient rivets to trans¬ 
fer the bottom chord stress, 54600 lbs. This requires— — ° =9 

6136 

rivets, making a total of 14 rivets in the bottom chord connec¬ 
tion. If the reaction acted equally on all the bottom chord 
connection rivets at this point, the connection would only have 
to be proportioned for the resultant of the two stresses 


\^64600 2 + 312 O 0 2 =62900 lbs., 


only be = 


62900 

6136 


rivets. 


and the rivets required would 


It is not good practice to put the rivets closer together than 
2y 2 in., and they must not come nearer the edge of any piece 
than 1 J /4 in. (7). Care must be exercised to see that the rivets 







94 


THE DETAIL DRAWINGS. 


Art. 41. 


in opposite legs of angles stagger so that one rivet head does not 
interfere with the driving of the other rivet. 

Joint C. At this point the components of the stresses in 
bC and Cd, parallel to the rafter, balance each other in the plate 
and require no rivets in the rafter. The components perpendi¬ 
cular to the rafter must be transmitted to Cc. Their sum is 
7000 lbs., which may be gotten by laying off the stresses and 
scaling the components parallel to Cc. The balance of the stress 
in Cc (=7000 lbs.) comes directly from the rafter. These to¬ 


gether require 14000 =3 rivets in bearing on the % in. gusset 

4690 

plate. There must be a sufficient number of rivets through the 
rafter angles to transmit the 7000 lbs. More are put in here 
so as not to exceed the maximum allowed pitch. 

It will be noted that the rivet spacing dimension line for 
each member starts at the center. A connection by a single rivet 
should never be used, and preferably at least three rivets should 
be used in any connection. 

Joint c. A splice is made here in the bottom chord because 
it changes section, and it is made a field .splice because the truss 
is too large to ship in one piece. Each truss is shipped in four 
pieces. The middle section of bottom chord and the vertical 
member Ee are two of these. The greatest depth of any piece 
will then be over 12 ft. at Cc, and this can not be handled by 
all railroads. (31) 

The horizontal components of Cc and cd act toward the 
right and their sum, equal to 15600 lbs., must be transmitted to 
be. (15600 lbs. is the difference in the stresses in be and ce.) 


This requires 


15600 

4688 


4 rivets in bearing on the % in. gusset 


81200 

plate. The bottom chord splice will require -= 11 rivets 

3068 

in single shear. We must have 11 rivets on each side of the 
splice, in the splice plate, which also acts as a connection for the 
bottom chord rods, strut and tie. The three rivets through ce 
and the gusset plate are not counted as a part of the splice 
(Spec. Art. 38) but are put in because there should be a connec¬ 
tion between the vertical as well as the horizontal legs of the 
angles. The splice plate should have as much net section as the 

i 





Art. 41. 


THE DETAIL DRAWINGS. 


95 


angles of ce. Even with the minimum thickness of plate allowed 
there is a large excess in this case. 

Lateral Connections. The lateral connections should be 
sufficient to take the full value of the area of a % in. rod at 
18000 lbs. per sq. in. (Spec. Art. 13). We have then 0.44X18000 
=7900 lbs. If we use a 1% in. pin for the lateral rods which 
have forked loops, the allowed bearing pressure of the pin on 
the i/ t in. plate will be i/ 4 Xl 3 /4 X25000=10900 lbs. 

It is very essential that clearance be provided where two 
members come together, except where tight joints are required, 
as in the bottom chord splice and at the ridge. The usual mini¬ 
mum clearance of members is % in. 

Rivet holes are made T y in. larger in diameter than the size 
of the rivet to be used. In roof work for lateral connections, 
pin holes are usually punched, and are made in. larger than 
the pin. Sizes of all rivets and holes must be plainly marked 
on the drawings. 

The exact length of each piece must be given with its other 
dimensions. The length should invariably be given last. The 
width of a plate should be given first and the longer leg of an 
angle should be. given first, thus, 1—15"X%"X1'—7%", 

2ZA 4"X3"X n> ,/ X21 / —7%". The width of a plate should al¬ 
ways be given in inches, and should not contain a fraction less 
than % in. 

For the use of the templet maker, the bevel of each in¬ 
clined line of rivet holes should be given. The longer dimension 
of the bevel is usually made 1'—0". All dimensions, other than 
the widths of plates, of one foot or more should be given in feet 

and inches, and not in inches alone, thus 1'—liV and not 
iq 3 " 

1 O 1 £ 

While no dimension is ever to be taken by scale, off a shop 
drawing, it is nevertheless essential to draw by scale. This can 
not be done unless the drawing is worked up in a logical man¬ 
ner. A draftsman who makes many erasures will seldom be¬ 
come interested enough in his work to be a success. Rivet heads 
and rivet holes should be drawn to scale. 

Accuracy is essential, but no smaller fraction than ^ of an 
inch is ever used in structural work. If a line of spacing should 
add up 10'—6J|", 10'—6 1 //' will not answer. 


96 


THE DETAIL DRAWINGS. 


Art. 41. 


All spacing must be continuous from center to center, and 
the different sets of spacing should be kept separate and in 
straight lines, if possible, not offset lines. First we have the 
general dimensions such as span and length of rafter, center to 
center; second, we have the distance center to center for each 
member; third, we have the rivet spacing which must be con¬ 
nected with the centers; and fourth, we have the open holes, 
which should be connected up for the benefit of the inspector. 
If there are holes in both legs of an angle, there must be two 
lines of spacing. 

Each rivet hole must be located definitely, cuts on plates 
shown, and bevels of center lines given. The gages of all rivet 
lines must be given. , 

The good appearance of a drawing goes far to inspire con¬ 
fidence in its accuracy. It should be workmanlike. The ap¬ 
pearance of a drawing depends largely upon the lettering and 
general arrangement. Except in the title, the letters should all 
be free hand and of a plain style. The figures should be par¬ 
ticularly clear. Figures and letters should not all be the same 
size. The dimensions of a main member should be in larger 
figures than those for a detail, and center distances larger than 
rivet spacing. It is essential that the sizes of plates, angles, etc., 
be in the best possible place for them. Shop men are not sup¬ 
posed to be able to read a drawing as readily as a draftsman 
or templet maker. To become a proficient letterer, persistent- 
practice is necessary, and will work a wonderful improvement 
in any man’s work. (27) 

The title and sheet number should be in the lower right 
hand corner, if possible. The name of the draftsman and the 
date when the drawing was finished, should appear in the title, 
as well as a statement of what is shown on the drawing. (See 
Fig. 24.) 


97 


98 




f»r" ' 


Ont/f on 


W Pinhole /$ 


n 

M 

X 

k* k 

7SL 

g 

v 

A 

<* in 

k! k 

v! 

k 

g 

A 

k 

2V? 

X 

X 

0: 

k r 

k 

k 

£ 


s k 
k k 

k 

k 

g 

6 

/\ 

& 



Fig. 3G. 



















































































































































































CHAPTER Y. 
PLATE GIRDER BRIDGES. 


42. Construction and Uses. A plate girder is a built up 
I-beam. It consists of a single web plate 1 and two flanges (top 
and bottom) riveted together. Each flange may be composed 
of two angles, two angles and one or more cover plates, two 
angles with side and cover plates or, in very heavy girders, four 
angles with side and cover plates in various combinations. Fig. 
37 shows some common flange sections. Types (e) and (f) are 
frequently used for crane girders where a load is applied along 
the edges of the flange. 





(c) (d) 

Fig. 37. 


Pn 


pi»—1— 


(e) 


(f) 


Plate girders are used in buildings and bridges where some¬ 
thing larger than a rolled I-beam or I-beam girder is required. 
In buildings they are used for floor and crane girders and in 
bridges, for stringers and floor beams, and for the girders ot 
plate girder bridges. 

Plate girder bridges are seldom built for spans of more than 
100 ft., though some have been built over 130 feet long. The 
railways use them almost exclusively for spans from 30 ft. to 
100 ft., when steel bridges are used, and many of the better class 
of highway bridges of these lengths are plate girders. 

A plate girder bridge is usually considered to be the most 
durable kind of metal bridge. 

43. Stresses in Girders. 2 A plate girder is treated as a 
solid beam and the stresses are investigated by the method of 

3 When two web plates are used a few inches apart, it is called 
a box girder.” 

2 See Heller’s Stresses in Structures,” Art. 75, page 111. 

> o 

j i > 

* , > 


99 






































100 


STRESSES IN GIRDERS. 


Arfc. 43. 


sections, 1 2 the stresses acting' upon a cross section being the ones 
usually found. 


The loads, including the weight of the girder itself, which a 
girder carries, together with the reactions produced by them, are 
usually a series of forces parallel to the cross section of the 
girder, and are equivalent to a resultant shear at the section and 
a couple; these are held in equilibrium by a shearing stress and 

a couple acting in 
opposite directions 
at the section. This 
is illustrated in Fig. 
38, in which R at c 
is the resultant of all 
forces to the left of 



equivalent to the 
shear II at the sec¬ 
tion and the couple 
whose moment is Ra and is called the bending moment. These 
are resisted by a shearing stress S, equal to R and a moment of a 
couple Fd—Ra. Since the bending moment is the moment of a 
couple, the moment of the bending stresses must also be that 
of a couple. The forces F are the resultants of the tensile and 
compressive forces acting on the section, whose intensities vary 
uniformly from zero at the neutral axis to a maximum intensity 
at the top and bottom. Since the greater part of the area of the 
cross section is in the flanges and the intensities are greatest at 
the top and bottom, the resultants, /' 7 , come near the top and bot¬ 
tom of the girder, making d large. Fd is the moment of resist¬ 
ance, and it is well to remember that it is equivalent to the 
moment of a couple, and that both the web and flanges resist 
bending. 


44. The Web. It is not known just how the shearing 
stresses are distributed over an I cross section. We know that 
their intensities must be zero at the upper and lower edges of 


’tSee Heller’s “Stresses in Structures,” Art. 64, page 85. 

2 See Heller’s “Stresses in Structures,” Fig. 65, page 86. 



























Art. 44. 


THE WEB. 


101 


* 


the girder, and are a maximum at the neutral axis. 1 The law 
of variation between these extremes depends upon the cross 
section. For an I cross section, the usual assumption that the 
shearing stress is uniformly distributed over the area of the web 
only, will give an intensity of shearing stress which will usually 
be greater than the actual maximum. 2 The flanges form a large 
part of the cross section and must carry considerable shear. 

It is therefore always assumed that the web carries all of 
the shear 3 and that its intensity is uniform. 

Av=ht— .(I ) 4 

Ss 


Equation (1) will determine the minimum area of web per- 
missable. Its thickness is never made less than *4 inch and 
seldom less than % inch. It must be made thick enough to give 
sufficient bearing for the rivets which connect the flanges to it, 
and this consideration frequently determines its thickness. 5 

The depth, h, is determined by considerations of economy as 
explained in Art. 46, or by local conditions. 

When there are splices in the web, it is not strictly correct 
to take the gross area as effective in resisting shear. It may be 
assumed that the rivets of the first row in the splice take up 
one half of their proportion of the shear on one side of the plane 
through the center of the row. (4) Then the net section of the 
wOb through this row should be sufficient to take the balance of 
the shear. This would make equation (1) read as follows: 

- -- —{h—holes) t .(2) 


Ss 


Formula (2) is not used in practice, and the difference in 
the result by the two is usually negligible. 


x For a discussion of this subject on the assumption that a sudden 
change in width of the cross section has no effect upon the distribu¬ 
tion of the shearing stress, see Johnson’s “Modern Framed Struc¬ 
tures,” Chapter VIII, Art. 130, page 145. 

See also Rankine’s “Applied Mechanics,” Art. 309, page 338. 

2 See Heller’s “Stresses in Structures,” Art. 71, page 105. 

3 When the flanges are inclined, they carry a part of the shear. 

4 See Heller’s “Stresses in Structures,” Eq. 33, page 111. 

5 See an article by C. H. Wood in Eng. News, Aug. 6, 1908. 







102 


THE FLANGES. 


Art. 45 


The web resists considerable bending moment, as will be 



seen if the formula 


is considered. If, for example, the moment of resistance of the 
web is \ of the total moment of resistance of the cross section, 
the web will resist ^ of the total bending moment and the flanges 

will resist of it. The resultant of the two kinds of stresses 
in the web is never calculated, but to compensate for this, it is 
often assumed that the flanges take all the bending stresses, 
which, of course, has the effect of making them larger and thus 
reducing the stress in the web. But if it be remembered that 
the shear is not a maximum where the bending is, it will be seen 
that, theoretictally, this increase of flange section is not neces¬ 
sary. 

45. The Flanges. The bending stresses in a girder may 
be provided for by making the cross section such that the ex¬ 
treme fiber stress, given by equation (3) will not exceed the 
maximum allowed unit. This, however, involves much labor, 
as there are no complete tables of section moduli of plate girders 
as there are of I-beams, and the solution, involving the two un¬ 
known quantities 7 and v . must be by trial. 

When the flanges are alike, as they usually are, the solution 
is very much simplified by making two assumptions: 2 

“1. The stresses in the flanges (tension and compression) 
are uniformly distributed over their areas and their resultants, 
( F , Fig. 38) therefore, act at the center of gravity of these areas. 

“2. That the depth of the web li, may be set equal to d, 
the distance between the centers of gravity of the flanges.” 

Granting these, it is easily shown that the moment of re¬ 
sistance of the web is equal to the moment of resistance of y rt 
of the web area, concentrated at the center of gravity of each 
of the flanges. 


’For derivation see Heller’s “Stresses in . Structures,” Art. 66 
page 89. 

"See Heller’s “Stresses in Structures,” Art. 75, page 111, for a 
complete discussion. 




Art. 45. 


THE FLANGES. 


103 


Then we have 


„ . , M 

Equivalent Flange Stress— .(4) 

Equiv. E'lg. Stress 


Equivalent Flange Area— 


(5) 


Rcqd. Flange Area proper (Net Area one Flange) 

—Equiv. Fig. Area — y 6 A w .(6) 

If, for any reason, there are vertical lines of rivet holes in 
the web, its moment of resistance is decreased, and this is some¬ 
times taken into account by modifying* Eq. (6) as given in equa¬ 
tion (7) below, 1 

Reqd. Flange Area proper (Net Area one Flange) 

=Equiv. Fig. Area—y^Ay, .(7) 


The effect of the rivet holes on the moment of resistance of 
the web may be easily calculated. 

Some specifications require that all of the bending stresses 
shall be considered as being resisted by the flanges, in which case 
the equivalent flange area as given by equation (5) becomes the 
required net flange area proper. 

Since d, the effective depth, cannot be calculated until the 
flanges are known, an approximate value must be used on the 
first trial. Two or three trials will usually give a flange which 
is practically exact. 

In equation (5) the working stress for the tension flange is 
used, thus giving the required net area, of that flange. (See 
Art. 11 for allowance to be made for rivet holes.) The top 
flange is usually made the same as the bottom flange (gross areas 
alike) but it must be held so that it will not buckle sidewise. 2 
(See Art. 51 and 52.) 


46. Economic Depth. 3 The most economical depth of a 
plate girder is usually the least weight depth. It depends upon 
a number of conditions and may be easily calculated, theoreti- 

callv, when these conditions are known. The calculated, economic 

• / 

’See Specifications of the “American Railway Engineering and 
Maintenance of Way Association.'’ for Steel Railroad Bridges, 1906, 
Art. 27. 

2 See Spec, of the Am. Ry. Eng. and M. of W. Assoc., Arts. 28 
and 78. Also Cooper’s Spec, for Steel Railway Bridges, 1906, Art. 79. 

3 See Johnson’s “Modern Framed Structures,” Art. 285, page 332. 









104 


ECONOMIC DEPTH. 


Art. 46. 


depth is seldom used exactly, on account of local conditions and 
practical limitations, and is to be regarded merely as a general 
guide. A variation in depth of as much as 10% or 15% will 
usually not change the total weight of the girder appreciably. 

Formulas will now be deduced for the economic depth for 
the following three conditions as to .flange section: 

(a) When % of the web area is considered in each flange. 

(b) When y 8 of the web area is considered in each flange. 

(c) When none of the web area is regarded as flange area. 
The girder will be assumed of constant cross section from 

end to end. 

(a) When % of the web area is regarded as flange area. 
The gross area of the cross section of the girder =ht-\- 


2 A f -f-rivet boles. From equations (4) and (6), A F 
and then we have, setting h=d, 


2 M 

A—dt -1- y 8 dt-\-rivet holes. 

dst 

The gross area of the flanges may be taken as 15% greater 
than the net area, which gives: 

2.3 M 

A=0Mldt+—r- 

ds t 


As the weight varies directly with the cross section, for a 
least weight depth we may differentiate this expression with 
respect to d and set the first derivative, equal to zero. 


d,A 

dd 


=0.6177- 


2.3 M 
s t d? 



from which 


72 ^ 

a —- and 

0.617* t 


<2=1.93 


3 V 


M 


St t 


( 8 ). 


• ( b ) When y 8 the web is taken as flange area, equation (8) 
becomes 


<7=1.80 




M_ 

Sf t 


( 9 ) 


(c) AY hen no web is considered as flange area, equation 
(8) becomes 

M~ 


(7=1.52 


\l 


St t 


( 10 ) 















Art. 47. 


STIFFENERS. ‘ 


105 


When the flange section is not constant for the entire length 
of the girder, the economic depth will be somewhat less than 
that given by the above formulas, and will vary with the propor¬ 
tion of cover plates, stiffeners, and web splices. The following 
equation will give the least weight depth as close as a general 


formula can give it. 




\ 


47. Stiffeners. The 


M 


St t 


( 11 ) 


ines of maximum compression in a 
plate girder web, cross the neutral axis at an angle of 45° and 
extend downward toward the supports from the middle. 1 The 
tendency of the web plate to buckle under these compressive 
stresses is, in part, resisted by the equal tensile stresses at right 
angles to them. Just what the resulting effect on the web is, is 
not well understood, but when the ratio of the depth of the web 
to its thickness is great (exceeds about 50 or 60) it must be 
stiffened. Of course the requirement of stiffeners depends upon 
the amount of shear at the point. 2 

Stiffeners are placed vertically on account of ease of manu¬ 
facture. They would, perhaps, serve their purpose better if 
placed parallel to the line of the compressive stresses, but if 
placed vertically and not more than the depth of the girder 
apart, or 5 or 6. feet for deep girders, they will prevent any 
buckling of the web. 

There is no rational method of determining the size of these 
stiffeners. Some specifications 2 give column formu¬ 
las for this but there is no rational basis for it. 

Practice only determines their size and spacing. 

Sometimes fillers are put under the stiffeners, 
between the flange angles, and sometimes the stiff¬ 
eners are “off set” or “crimped” over the flange 
angles as shown in Pig. 39. Fillers should be used 
under stiffeners bearing concentrated loads, or 
where there is*anything connecting to the girder 
bv means of the stiffener. 



Fig. 39. 


1 See Heller’s “Stresses in Structures,” Art. 73, page 109. 

Also see Johnson’s “Modern Framed Structures,” Art. 130, page 147. 

-iSee Cooper’s Specifications for Steel Railway Bridges, 1906, 
Art. 47. 

See also Spec, of the Am. Ry. Eng. and M. of W. Assoc., 1906, 
Art. 77. 
















106 


WEB SPLICES. 


Art. 48. 


Stiffeners should be placed at the ends of a girder, to trans¬ 
mit the end reaction from the web, and at all points of concen¬ 
trated loading. Stiffeners should bear tightly against the hori¬ 
zontal legs of the flange angles at all points of concentrated 
loading, as the load must be transmitted to the stiffener by direct 
bearing upon its end, and from the stiffener, by means of rivets, 
to the web. 

The outstanding leg of the stiffener should not project be¬ 
yond the edge of the flange angle, and the other leg need only 
be large enough for the rivets. 

48. Web Splices. For small girders, such as stringers 
and floor beams, the web plates can usually be obtained from 

the mills in one piece, 
and no web splices are 
necessary. When, how¬ 
ever, the size of the gir¬ 
der is increased, the 
web plates cannot be 
obtained in single 
lengths and must be 
spliced. 1 

The stresses carried 
by the web at the point 
must be transferred 
t h r o u gh the splice 
plates from one web 
plate to the other. If 
no bending moment is 
regarded as being car¬ 
ried by the web plate, 
only the shear has to be 
provided for, and the calculation of the rivets is a very simple 
matter. In this case a splice similar to that shown in Fig. 40 
is used. The rivets are usually not spaced over 5 inches apart, 
and usually two rows are used on each side of the splice, al¬ 
though this often gives an excess of rivets. 

^or maximum sizes of plates which may be obtained, see Cambria, 
page 31. These limits vary considerably with different mills. 



Fig. 40. 












































Art. 48. 


WEB SPLICES. 


107 


Two splice plates should always be used and their combined 
thickness should be greater than the thickness of the web. A 
pair of stiffeners is 'always placed over the splice. 

When a part of the bending moment is regarded as being 
carried by the web, the web splice must be designed to provide 
for this stress in addition to the shear. The simplest form of 
web splice to calculate, in this case, is that shown in Fig. 48, 
in which the plates FG, near the flanges, are assumed to take 
care of the bending moment in the web, and the vertical plates 
HK, are assumed to take all the shear. These assumptions give 
an excess of plate and of rivets, but a rigid calculation would 
make a splice of practically the same cost. See Art. 52 for the 
design of such a splice. 

In order that the allowed unit stress in the flange proper 
may not be exceeded, it is necessary to reduce the allowed unit 
stress in the splice plates FG, in proportion to their distance 
from the neutral axis. The entire solution must, in any case, be 
by trial. 

The form of splice shown in Fig. 40 may be used in place 
of that of Fig. 48, but the rivets must be calculated so that the 
resultant of the horizontal and vertical stresses (due to moment 
and shear) in the outermost rivets will not exceed the allowed 
stress on a rivet. (12) This would also be the exact method of 
calculating the rivets in Fig. 48. In Fig. 40 the splice plates 
act as a beam 8'— l 1 /^' deep to carry the web bending moment, 
and the extreme fiber stress in them must not exceed the unit 
stress in the girder at an equal distance from the neutral axis. 
If the rivets through the Aveb in the outer rows have a small 
pitch, one-eighth of the web area may not be available as flange 
area. 

49. Flange Riveting The stress in the flange of a girder, 
at the end, is zero, and it increases to a maximum somewhere 
between the supports (for a girder supported at the ends). The 
increase of the flange stress is due to the addition of the hori¬ 
zontal shears, 1 and the rivets connecting the flange to the web. 
at any point, must be sufficient to transmit this horizontal 
increment. 


>See Heller’s “Stresses in Structures,” Arts. 17 and 70. 



108 


FLANGE RIVETING. 


Art. 49. 


Fig. 41 shows any part of a. girder, supported in any man¬ 
ner. M and 8 are the known moment and shear at the section 
AB, then 

M x =M+S{x-m)—P 1 {x-a)-P,(x-b) —P s {x—c) 
Differentiating with respect to x, - will give the rate of 


dx 


increase of the moment along the girder 
dM x 


dx 


S-P.-P-P^S: 


AL 


The flange stress* at any point is— 1 and, therefore, the rate 

d 


of increase of the flange stress 


II? 


•n i dM x S_x 

will be —— — d 


(12. 


E 


-©-a 


Gt - 

b 


e-e 


-e-o- 


o-o- 




3-r 


c— 

V 


---*— 

A 

m 


h X-m ^ 




he-e- 

-©- 

o o o o-e—o-e-o- 


t M 
v5 


Fig. 41. 



dx " d 

or, in words, the increase of 
the flange stress per inch 
will be equal to the shear at 
the point divided by the ef¬ 
fective depth of the girder in 
inches and sufficient rivets must be provided, connecting the 
flanges to the web, to transmit this increment. Then, to obtain 
the maximum permissable rivet pitch in inches at any point, the 
value of a rivet must be divided by the increment per inch. (If 
there is no vertical load on the flange.) 

In a girder whose cross section is constant from end to end , 
and in whose design a part of the web has been considered as 
flange area, the pitch of the rivets may be increased because 
the part of the flange stress which is carried by the web does 
not have to be transmitted by the rivets. Since the flange 
stresses are directly proportional to the flange areas, we have 
from equation (12) when one-sixth of the web is regarded as 
flange area, 

S ■ A 

Increment of stress in flange prope)'=~y. --—.. (13) 

d A p-^-^Apy 

or when one eighth of the web is regarded as flange area, 

Increment of stress in flange propei±= — x-—- (14) 

d A F A^A tv 




































Art. 49 


FLANGE RIVETING. 


109 


In a girder with cover plates which do not extend the full 
length of the girder, and in whose design a part of the web has 
been regarded as flange area, equation (13) or (14) may be used 
for that portion of the girder at the ends, whose cross section is 
constant, but when, passing toward the middle, the first increase 
in flange section is made by the addition of a cover plate, the 
flange angles and the part of the web considered as flange area 
have already received their maximum allowed stress (See Fig. 
47) and, therefore, all of the flange stress increment must go 
into the cover plate and enough rivets to transmit it must be 
provided, both through the angles and web, and through the 
cover plate and angles. 

So far we have considered only the flange stress increments 
as affecting the pitch of the rivets. If there are any loads 
resting upon the flange of the girder, they must be transmitted 
to the web, and since the web plate is not flush with the backs 
of the angles, the rivets in the flange must perform this duty 
unless the load is carried directly by stiffeners. 

The lop flange of a deck plate girder is a case of this kind, 
and the resultant of the two stresses (vertical and horizontal) 
on a rivet must not exceed the allowed rivet value. 

Usually only three or four different groups of rivet pitches 
are used in the half length of a girder. The pitch need be fig¬ 
ured only at three or four points and then a curve can be drawn 
through these, which will give the pitch at any other point with 
sufficient accuracy. See Fig. 42 and Fig. 47. 

The riveting in the two flanges is always made the same 
when possible, although this gives an excess in the bottom flange. 

Sometimes the pitch of rivets in the flange angles will de¬ 
termine the width of the vertical leg of the angles which may 
be used. For instance, if 2 Ls 4"x4" would answer for the flange 
of a stringer, and it was found that the pitch of rivets required 
was less than the minimum allowed.in a single line, (7) an 
angle with a vertical leg wide enough for two gage lines would 
have to be used. 

Sometimes the thickness of the web plate will ha.ve to be 
increased over that which would be required to resist the shear, 
in order to provide sufficient bearing area for the flange rivets, 
so that they will not have to be spaced closer together than the 


110 


FLANGE SPLICES. 


Art. 50. 


minimum allowable pitch. Also the web must be thick enough 
so that there is sufficient net area, horizontally between the 
flange rivets, to carry the horizontal increment of flange stress. 
These considerations sometimes make it necessary to use a 
thicker web plate at the ends of a girder than in the middle. 1 

50. Flange Splices. There are two conditions which may 
make it necessary to splice the flange of a plate girder even if 
the girder is not going to be shipped in more than one piece. 
These are, 

1st. The flange angles may be so heavy that they cannot 
be obtained in one piece, of the length required. (26) 

2nd. When the girder is for a through bridge, frequently 
the upper cornel’s are rounded, for appearance, and the top 
flange angles and one cover plate run down the ends of the 
girder. In this case, the flange is spliced near the ends, so that 
the long pieces will not have to be handled in the blacksmith 
shop in heating, bending and annealing. 

The flange splices should always be made as near the ends 
as.possible, where the flange stress is least; and the joints in the 
component parts of the flange should break joints. (29) 

The splices are made by means of splice angles cut and 
ground to fit the inside of the flange angles and by splice plates 
on the top. The net section of the splice plates and angles does 
not have to equal the entire net section of the flange cut, unless 
the entire strength of the cut portion is required at the point of 
splice. The size of the splice plates and angles and the number 
of rivets required are determined by the proportion of the 
actual stress at the point, carried by the part cut. 

To illustrate the application of the principles set forth in 
this chapter, the design and methods of calculation for a stringer 
and a deck plate girder bridge, will now be given. 

51. Design of a Stringer. The stringer of a railroad 
bridge is the simplest form of plate girder. We will assume 
the following data: 

Panel length 27' —0", Stringers 6' —6" center to center, 

Loading Cooper’s Class E 40, 


3 See an article by C. H. Wood in Eng. News, Aug. 6. 1908. 



Atr. 51. 


DESIGN OF A STRINGER. 


Ill 


Specifications Cooper’s 1906 for Railway Bridges, 

Material medium steel except rivets. 

Dead Load. The dead load is estimated and consists of the 
weight of the floor (rails, ties, guards, fastenings, etc.) and the 
weight of the stringer itself. Except in special cases, the weight 
of the floor will not exceed 400 pounds per lineal foot of track, 
and the specifications §23 will not allow the use of a lesser 
weight. The weight of the stringer will be taken at 160 pounds 
per lineal foot. This gives a total dead load per lineal foot of 
stringer, of 360 pounds. 

The dead load moment= 360X27x27 __ 32 800 ft. lbs. 

8 ’ 

The live load moment (See Spec. Table I)=344,600 ft. lbs. 1 

Depth. The depth of the stringer must now be decided 
upon. The economic depth may be determined from equation 
(10), as §46 of the specifications directs that no part of the web 
area may be considered as flange area. The value of s t to use in 
Ihe formula is determined from §31 of the specifications, and is 
different for live and dead loads. The dead load moment may 
be reduced to an equivalent live load moment, in this case by 
dividing it by 2, and then the live load unit stress may be used 
with the resultant total moment. This will give a total equiva¬ 
lent moment of 361,000 ft. lbs. Assuming the web to be %" 
thick we get 

d= 1.52 x j 361 Qn °X 12 — 51.6 inches. 

\ 10000XM 

If there are no local conditions which will limit the depth 
of the stringer, such as the height from base of rail to masonry, 
under clearance or depth of floor beam, we can use a 51" web 
plate. This will give an area of Aveb of 5lX%=10.13 sq. in. 

The maximum shear is as follows: 

Live load end shear—59,300 lbs. (See Spec. Table I) 

Dead load end shear= 4,900 lbs. 

Total Max. end shear=64,200 lbs. 

64200 

This will give a maximum unit shear on the web of — : — = 

19.13 

3,360 lbs. per sq. in., which is safe. 

1 

J For method of calculation of maximum moment see Heller’s 
“Stresses in Structures,” Art. 134, page 260. 








DESIGN OF A STRINGER. 


Art. 51. 


112 


The depth back to back of angles is always made *4" more 
than the depth of the web plate (26) so that the web will not 
project beyond the angles at any point. 1 An approximate effec¬ 
tive depth must now be assumed (45) for determining the re¬ 
quired flange. We will take 50.5 inches. 


Flanges. The following are the approximate flange stresses: 

32800 X 12 

Dead Load—-= 7,800 lbs. 

50.5 

344600 X 12 

Live Load =-=81,900 lbs. 

50.6 

Dividing these by their respective unit stresses we get, 

7800 

Approx. Req. D.L. Area=- ==0.39 sq. in. 

20000 

81900 

Approx. Req. L.L. Area^=-=8.19 sq. in. 

10000 

Approx. Req. Total Net Area =8.58 sq. in. 

2Ls6"X3y 2 "XiV' g^es 2X5.03—2X i 9 « X1 =f= 8.93 sq. in. 
Net (using %" rivets). 


The effective depth, using these angles with the long legs 
horizontal, will be 51.25—2X0.86=49.53 inches. This will give 
the following flange stresses, 


Dead 

Live 


Load= 


Load = 


32800 x 12 
49.63 

344600 X 12 
49.53 


= 8.000 lbs. 
=83,500 lbs. 


and the required areas will be 

8000 

Dead Load Area=- =0.40 sq. in. 

20000 

83500 

Live Load Area^=-=8.35 sq. in. 

10C00 

Total Req. Net Area=8.75 sq. in. 


’Sometimes on stringers without cover plates, the wet) is made 
to project an inch above the top flange angles and the ties are notched 
;for this instead of over the entire flange. 














Art. 61. 


DESIGN OF A STRINGER. 


113 


It will be found that the flange section above given is the 
most economical for this case. The actual net area only exceeds 
the required by 0.19 sq. in. 1 

We must now determine the rivet pitch in the flanges in 
order to see if we can get the required number of rivets in a 
single line (49) without using a less pitch than is allowed. 
(See Spec. §54). (7) 

Flange Riveting. Total Max. End Sheai—64,200 lbs. 

The horizontal increment of flange stress from equation 
. 64200 

(12) is-=1296 lbs. per lineal inch. The top flange also 

49.53 

carries the weight of the floor and the live load direct, which 
must be transmitted to the web through the flange rivets. (49) 
The dead load on the top flange is 200 lbs. per lineal foot, equal 
to 17 lbs. per lineal inch. The maximum concentrated live load 
on any point of the stringer will be one driver or 20,000 pounds, 
which mav be considered as distributed over three ties (See 
Spec. §15) spaced 14 inches center to center, making the load 
20000 

per inch-=476 lbs. This makes the total maximum vertical 

3X14 

load on the top flange 493 lbs. per lineal inch. The resultant 
of these vertical and horizontal stresses= ^ (493) 2 4- (1296) 2 = 
1387 lbs. per lineal inch. 

The value of a rivet in bearing on the web is 3938 pounds. 

(See Spec. §40, floor system.) The maximum allowed pitch 

3938 

at the ends then will be-= 2.83 inches, which is greater than 

1387 

three diameters of the rivet and is, therefore, allowable in a 
single line. 

The required pitches may be determined in a similar man¬ 
ner at the quarter point and center after the shears at these 
points have been calculated, and when plotted, as in Pig. 42, we 
can scale the required pitch at any point. The actual pitches 
used should come within the curve, as shown by the stepped line. 

Un some cases, the bottom laterals of the bridge are connected to 
the bottom flanges of the stringers, in that case the net section is re¬ 
duced by an extra hole out of the horizontal leg of one flange angle. 









114 


DESIGN OF A STRINGER. 


Art. 51. 


Stiffeners. According' to the specifications, §47, the web 

must be stiffened when the 
shearing stress per square 
inch exceeds 10000—75 H, in 
which E is the ratio of the 
depth of the web to its thick¬ 
ness. Bv this formula, the 
maximum allowed shearing 
stress on this web, without 
stiffeners, is a negative quan ¬ 
tity, so stiffeners must be used throughout the length, spaced 
not more than the depth of the girder apart (Spec. §47). We 
will have to put in six pairs of intermediate stiffeners in order 
to keep within this limit. 

The size of the stiffeners must be determined bv the column 
formula given in the specifications §48. The smallest angles 
which can be used with %" rivets have 3" legs ( Cambria , page 
54) and the thinnest metal allowed is %" thick (Spec. §82), so 
for the stiffeners we will try 2 Ls 3"X3"X% /r - The radius of 
gyration of the stiffeners, fillers and enclosed web, perpendicular 



Fig. 42. 


to the web is 1.35 in. P=10000- 


. - l 
4o 

r 


T0000—45 


51 

1.35 


-8300 lbs. 


per sq. in. The gross area of the stiffeners, fillers and enclosed 
web is 8.72 sq. in., therefore, the stiffeners are good for a shear 
of 8.72X8300=72300 lbs., which is greater than the maximum 
shear in the girder. 

The specifications §79, require that the compression 
flanges of beams and girders shall be stayed against transverse 

crippling when the 



JL X/11 Li.1 LllvJi. C L-llfl X J 

sixteen times t h e 
width. In this case 


have an unsupported 
length of about 16 
feet. They may be held by means of a cross frame at the middle, 
making the unsupported length 13 y 2 feet, or by means of a 
subdivided Warren lateral system of single angles between the 
top flanges, as shown in Fig. 43, making the unsupported length 



















Art. 51. 


DESIGN OF A STRINGER. 


115 


of the flange about 9 feet. The size of these angles may be 
determined by the minimum requirements of the specifications 
§§82 and 83. A common size is 3i/2 r/ X3"X%". 

If the track is on a curve, these angles must be made large 
enough to take care of the centrifugal force. 1 

Estimate of Weight. An estimate of the weight of the 
stringer will now be made to see how it compares with the 
weight assumed in the dead load. (160 lbs. per foot) 

Flanges 4 Ls 6"X3%"X*" @ 17 -! = 68.4 lbs. per foot. 

AVeb = 65.0 lbs. per foot. 

Stiffeners 2 Ls 3"X3"X% // (Equivalent) = 22.6 lbs. per foot. 
Bracing 1 L 3 1 /o"X3"X%" (Equivalent)— 5.0 lbs. per foot. 

161.0 lbs. per foot. 

Rivets, say 3%= 4.8 lbs. per foot. 

Total=165.8 lbs. per foot. 

This is near enough to the weight assumed so that no re¬ 
calculation will be necessary. 

In all cases the assumed dead load should be checked with 
the final estimate to make sure none of the actual stresses will 
exceed those provided for in the design, and also to see if any 
excess of material has been used over that actually required. 

No web splices are necessary, as the web plates can be ob¬ 
tained from the mills in one piece. (See Cambria , page 31.) 

52. Design of a Deck Plate Girder Bridge. The following 
data will be assumed: 

Span, 103 ft. Extreme (100 ft. c. to c. of bearings). 

Loading, Cooper’s Class E50. 

(Specifications, American Railway Engineering and Mainte¬ 
nance of Wav Assoc., 1906. 

«/ 

The width center to center of girders should not be less 
than about fa the span, and should never be less than six feet 
for a standard gage track. We will use a width of eight feet 
center to center. 

Floor. The ties will be made 8 inches wide, spaced with 
six inch openings (Spec. §5). The maximum driver load will 

] See Heller’s “Stresses in Structures,” Art. 166, page 307. 




116 


DECK PLATE GIRDER BRIDGE. 


Art. 52. 


be that due to the special loading (Spec. §7) and will be for 

one rail—v — 0000 =31,200 lbs. This is assumed to be distributed 
4 2 

over three ties (Spec. §5), making a pair of loads of 10,400 lbs. 
each on each tie, besides the dead load. To this must be added 
100% of the live load for impact (Spec. §5)' and the dead load 
^ A j may be taken at 200 lbs. at each rail 
J ^ ^ ’ for each tie, making a total of 21,000 

X 1 ^ pounds at each rail. The maximum 

moment on the tie will be IV 2 X 21000 = 
31,500 ft. lbs. See Pig. 44. Substituting 


f /.s. 


,3.0 c.A>c. G/ra/era- 


Fig. 44. 


*7 


in the formula M= (Equation 3, Art. 44) we can solve for 


v 


the depth of the tie directly. 

8 d 3 

2000 x- 


31500X12= 


12 


\d 


from which (Z“=141.75 d=11.9" 


The ties, therefore, will be 8"X12"XH ft- long, spaced 
14" center to center. 

Bead Load. The weight of the floor can now be calculated 
(Spec. § 6 ). 

Ties 8 "X 12"X ll'=396 lbs. each - fi ——=340 lbs. per lin. ft. of Br. 

14 

Guards 2— 6 "X 8 " 8 XTV 2 — 36 lbs. per lin. ft. of Br. 

Rails and fastenings —150 lbs. per lin. ft. of Br. 

Total weight of floor=526 lbs. per lin. ft. of Br. 


The weight of the steel work may be estimated by compari¬ 
son with similar structures, of which the weights are known, or 
may be approximately determined from an empirical formula 
of the form 

w—aL-j-b 1 (15) 


In the above formula “b” represents that part of the metal 
work, the weight of which does not vary appreciably with a 
change in span length, and may be taken at about 200 lbs. in 
the present example, and “a” we will assume as 12 . 5 . 


*See Heller’s “Stresses in Structures,” Art. 118, page 219. 

See also Johnson’s “Modern Framed Structures,” Art. 62, page 43. 











Art 52. 


DECK PLATE GIRDER BRIDGE. 


117 


The weight of the steel work=12.5Z+200 

=1450 lbs. per lin. ft. of Br. 
The weight of the floor, from above= 526 lbs. per lin. ft. of Br. 


Total dead load=1976 lbs. per lin. ft. of Br. 

Stresses. (43) The maximum live load moments and 
shears should be calculated at several points in the girder. Then 
a curve can be drawn through these values when plotted, which 
will represent the values at all points sufficiently close. 




*501 


3 




The maximum moment (near the center) and maximum 
shear (at the end) in the girder, should be calculated from the 
actual wheel loads 1 , and then the moments and shears at the 
other points may be calculated from equivalent uniform loads 2 
derived from this maximum moment and shear. 

The maximum 
moment will occur 
with wheel 12 pear 
the center of the 
Big- span (see Fig. 45) 

and the center of gravity of all the loads on the span must be 
as far on one side of the center as wheel 12 is on the other. Then 
from Fig. 45 we can write the following equations: 




£ 0 '. 



M a + W A £+ 


wx 


,*2 


W A -j-wx 


50 + 


2 


40+2=50-- 

*> 

)/ =Moment about A of all loads to the left of A, on the 

span. 

yp =Sum of all loads to the left of A, on the span. 

A 

^•-—Uniform load per lineal foot. 

Substituting in the above equations and solving for e and x, 
we get e=0.2 ft. #=9.9 ft. 

Having determined the position of the loads, the calculation 
of the moment is a simple matter. The work may be greatly 
facilitated by the use of a moment table if one is available. 


. ’See Heller’s “Stresses in Structures,” Art. 134, page 260. 
2 See Heller’s “Stresses in Structures.” Art. 144, page 269. 














118 


DECK PLATE GIRDER BRIDGE. 


Art. 52. 


The maximum live load moment in the girder is 4,025,000 
ft. lbs. 

The maximum live load end shear will occur with wheel 2 

9 

at the end of the girder, and is 187,500 lbs. 

The equivalent uniform load for moments is determined by 

w j2 

setting the maximum live load moment equal to - and solving 

8 

for w. 


4,025,000= 


w X10000 
8 


w =3220 lbs. per lin. foot of girder. 
The equivalent uniform load for shears is obtained by set- 

wL 

ting the maximum live load end shear equal to — and solving 

2 

for u\ 


187,500= 


w X 100 
2 


w==3750 lbs. per lin. foot of girder. 

From these equivalent uniform loads, the stress at any point 
can be obtained with sufficient accuracy. 

The uniform load moment varies as the ordinates of a para¬ 
bola., and can be scaled from a diagram drawn as shown in 
Fig. 47. 

The shears will now be figured from the equivalent uniform 
load at points 16 § ft., 33% ft., and 50 ft, from the end, 
(selected on account of the location of the web splices as deter¬ 
mined later.) 

' « 

For location of points A, B, C and D see stress sheet, Fig. 53. 

Live load shear at ,4=-— 2 =187,500 lbs. 

100 X 2 

Live load shear at B= 3750 ^ 83 : 3 - =130,200 lbs 

100X2 

lave load shear at C= 3750x66 • V — 83,300 lbs. 

100X2 

Live load shear at 7)= 3 - 750 ^ 50 = 46,900 lbs 1 

IOOiX 2 


3 The live load shear at D calculated from the actual wheel loads 
is 49,200 lbs., or 4.9% greater than that given by the equivalent uni¬ 
form load. 












Art, 52. 


DECK PLATE GIRDER BRIDGE. 


119 


To each of the stresses thus far determined, must be added 
the impact stress as determined by the formula given in the 

specifications §9, I—S 30 °— 

L + 300 


Summary of Stresses. 

Maximum Live Load Moment—4,025,000 ft. lbs. 


Impact= 


4025000 X 300 


Dead Load 


100 -f 300 
19 76 X 100 >< 100 
8 X 2 

Total Maximum Momen 


=3,018,800 ft. lbs. 

=1,235,000 ft. lbs. 
=8,278,800 ft. lbs. 


Live Load End Shear=187,500 lbs. 

x , 187500X300 -t a s\ caa i'u 

Impact=-=140,600 lbs. 

100 + 300 

Dead Load= i 976 x 100 = 49 400 lbs. 

4 --- 

Total End Shear =377,500 lbs. 
Live Load Shear at R=130,200 lbs. 


Impact= 


130200 X 300 

83X + 300 


=102,000 lbs. 


D.L.=49400—Vs X49400=32,900 lbs. 


Total Shear at B = 

Live Load Shear at C= 

T , 83300 X 300 

Impact— --— = 

66% -f 300 

D.L =49400- 2X49400= 

O 

Total Shear, at C — 

Live Load Shear at D— 

T , 46900 X 300 

lmpact=- = 

50 + 300 

Dead Load Shear = 


=265,100 lbs. 

= 83,300 lbs. 
= 68,200 lbs. 
= 16,500 lbs. 

=168,000 lbs. 

: 46,900 lbs. 

= 40,200 lbs. 

= 000 lbs. 


Total Shear at D = 87,100 lbs. 

Depth. The economic depth (46) can now be figured from 
equation (11), assuming the web to be % inches thick. 

( 1 = 


, 1 12 X 8278800 10Q7 . u 

= + ——-=128.7 inches. 

\ 16000 X % 


/ 


















120 


DECK PLATE GIRDER BRIDGE. 


Art. 52. 


The cost per pound of plates increases very rapidly as the 
width increases, after 100 inches is passed, until at 130 inches 
wide the cost has reached about 40% excess per pound over the 
cost of plates 100 inches wide and less. Also it must be remem¬ 
bered that pieces over about ten feet deep cannot be shipped on 
many roads, (31) so we will make the web of the girder only 
120 inches deep, instead of the depth given by the formula. 
This is probably more nearly the least cost depth, than that given 
by the formula, in this case. 

Web. The web plate will have to take the shear (44) with¬ 
out exceeding a unit stress of 10,000 lbs. per sq. in. on the gross 


area (See specifications §18). The required area will be 3775Q0 . 

r 10000 
87 75 

75 sq. in. - 1 — : ——0.315 inches required thickness, so we can 
120 


=37. ^ 


use a web plate 120"x%". 

Flanges. According to the specifications §27, one-eighth 
of the gross web area may be regarded as flange area. (45). 
For an approximate effective depth 10 ft. will be assumed. This 
gives a flange stress of 827,900 lbs. The approximate required 

area will be -=51.74 sq. in. net. 

16000 

The following flange section will be tried: 

o o 

Sq. in. gross Sq. in. Net. 

i/ s Web=%X45.00= 5.62 5.62 

2 Ls 8"X8"X 7 / 8 " =26.48 26.48-6XlX%=21.23 

1—20"X%" =10.00 10.00—2X1X%= 9.00 

1—20"X%" =10.00 10.00—2X1X%= 9.00 

1—20"XiV' = S-75 8.75—2X1X re = 7.87 

Total gross=60.85 Total net=52.72 


The net areas here have been figured with two rivet holes 
out of the vertical legs of the angles and one out of each hori¬ 
zontal leg. (11) To obtain this as a minimum net area the 
pitch of the rivets in the .cover plates must never be less than 
about 2% inches. 

The location of the center of gravity of this flange is 0.74 
inches from the backs of the angles as shown in Fig. 46, making 
the actual effective depth 120.25—2X0.74=118.77 inches. 






Art. 52. 


DECK PLATE GIRDER BRIDGE. 


121 


The actual flange stress then i s 8278800 

118.77 

=836,500 lbs., making the required area= 

- 3650Q =52.28 sq. in., so the above flange 
16000 1 

section will answer. 

Length of Flange Plates. The required 

lengths of the flange plates may be calcu- 

• Fig. 46. lated from the equation of the parabola, in 

this case, as we are using the equivalent 

uniform load for the moments. Or the 

lengths may be determined graphically by drawing the parabola, 

as shown in the upper diagram of Fig. 47. The graphic method 

is nearly always used, as the moment diagram is frequently not 

a simple curve. 



As the moments and required flange areas are directly pro¬ 
portional, (when the effective depth is constant) the areas will 
vary as the ordinates of a parabola also, and it is simpler to lay 
off areas as ordinates instead of moments. Any convenient 
scales may be chosen for lengths and areas. In this case the 



/ 


















































122 


DECK PLATE GIRDER BRIDGE. 


Art. 52. 


middle ordinate of the parabola is 52.28 (=Reqd. net flange 
area) and the curve may be drawn in any one of several ways, 
the method shown is a simple one. 

After the curve of required areas is drawn in, the net areas 
of the component parts of the flange are measured off on the 
center line and horizontal lines through these points represent 
the parts. The required lengths of the various pieces may now 
be scaled off directly. The flange plates are made 2 or 3 feet 
longer than the theoretic length in order to provide a few rivets 
through the plate near the ends so that the strength may begin 
to be effective where it is required, and also to compensate for 
the fact that the actual wheel loads give slightly larger moments 
near the ends than the equivalent uniform load. The effective 
depth decreases a little toward the ends, owing to the omission 
of the flange plates, and this will also make the flange stress a 
little greater there than is given by the parabola. 

For a symmetrical girder, only one half the diagram need 
be drawn. 

The top flange plate next to the angles is nearly always run 
the full length of the girder, to cover the flange angles and to 
stiffen them near the ends, against the deflection of the ties. 
(See specifications §76.) 

Scaling from the diagram, Fig. 47, the following are the re¬ 
quired lengths of the flange plates: 

20' / X 1 /2 ,/ —70 ft. use 74 ft. 

20"X%"—56 ft. use 60 ft. 

20"XtV'- 38 ft. use 42 ft. 

Flange Riveting. (49). The horizontal increment of flange 
stress at A (See Fig. 53) may be determined from equation (14). 
As the top flange also carries the direct load of the floor and 
live load the required pitch will be less for it than for the bot¬ 
tom flange, so the bottom flange pitch need not be figured. 

it • j -I • + 377500 36.48 OD1on 

Horizontal increment—--X-=2812 lbs. per lin. in. 

116 31 42.10 F 

The gross areas are used for proportioning the stress. Note 
also that the effective depth here is less than at the middle of 
the girder. 

The vertical load from the floor is 263 lbs. per lineal foot 
and the weight of the flange of the girder here is 127 lbs. per 



Art. 52. 


DECK PLATE GIRDER BRIDGE. 


123 


lineal foot, making a total dead load of 

390 lbs. per lineal foot— 33 lbs. per lin. in. 

Live load (See Spec. §§ 5 and 29)- 25000 

Impact (See Spec. §5)=100% 


42 


= 595 lbs. per lin. in. 


— 595 lbs. per lin. in. 

Total vertical load—1223 lbs. per lin. in. 

The total resultant stress on the rivets will be 
l/(2812) 2 +( 1223) 2 —3066 lbs. per lineal inch. 


Required rivet pitch- 


7876 _ 
3066 


=2.57 inches. 


To find the horizontal increment of flange stress at B, we 
must use equation (12) because the web is here carrying all the 
bending stress allowed, and all of the increment goes into the 
flanges proper. 

265100 


Horizontal increment 


=2266 lbs. per lineal inch. 


117.01 

Vertical load (same as before)=1223 lbs. per lineal inch. 
Resultant Stress=|/l223 2 -f2266 2 =2575 lbs. per lineal inch. 

7876 


Required rivet pitch= 


2575 


-3.06 inches. 


Horiz. increment at C= 1 - 68000 =1415 lbs. per lineal inch. 

118.77 

Resultant Stress= j/ 1223 2 +1415 2 =1870 lbs. per lineal inch. 

7876 

Required rivet pitch=-=4.21 inches. 

1 1870 


Horiz increment at D— 


87100 

118.77 


= 733 lbs. per lineal inch. 


Resultant Stress= j/ 1223 2 + 733 2 =1426 lbs. per lineal inch. 

Required rivet pitch=-j^j=£.52 inches. 

These rivet pitches are plotted as shown in Fig. 47 and the 
actual pitches used are made to come within the curve as shown 
by the stepped line. 

The required pitch of rivets through the flange plates is 
determined by the horizontal increment of flange stress alone. 
The total shear at the theoretical end of the first flange plate is 

276,000 lbs. This gives a horizontal increment oi -- =2360 


117.01 














124 


DECK PLATE GIRDER BRIDGE. 


Art. 52. 


I 


lbs. per lineal inch and a required rivet pitch 


Qf 2X7216 =61 
2360 


inches. As the maximum allowed pitch is 6 inches (See specifi¬ 
cations §37) it will not be necessary to calculate the pitch at 
any other points. The pitch of the rivets in the cover plates 
must bear some relation to that of the rivets through the verti¬ 
cal legs of the flange angles so that they will not interfere. (29) 

Flange Splices. (50). About the maximum length of 
angle 8"x8"x%" which can be obtained in one piece is ninety 
feet, therefore the flange angles will have to be spliced. We 
will splice one angle of each flange about 25 feet from each end 
of the girder so that both angles of one flange will not be cut 
at the same point. 

At this point the flange angles are carrying the maximum 
allowed stress, and the total stress in one angle will be 
10.61 X 16,000=169,800 lbs. 

To take this stress we will use a splice angle on the inside 
of the angle spliced and a plate inside of the other angle. The 
splicing material required, then, will be 1L 8"x8"x {J'' cut down 
to 7"x7"x }- J-" and ground to fit the fillet of the flange angle and 
one plate These will have an available net area of 10.53 

sq. in. The length of the angles will have to be sufficient to take 
enough rivets to transmit 169,800 lbs., and one-third of this must 
be transmitted to the plate on the side opposite the angle cut. 
According to the specifications §55, the rivets connecting this 
plate must be increased 66%% over the number required by 
§18 for the angle in contact with the cut member. 


Stress in one leg of splice angle= 


169800 

3 


=56,600 lbs. 


Rivets required in angle on side next to splice= =7.85 

7216 

66% ( /c =5.25 

Rivets required in angle on opposite side * =13.1 

The rivet pitch at the splice may be made 3 inches, which 
gives us a splice plate 6\L ft. long on the side opposite the splice 
and an angle 4 ft. long on the side next to the splice. 

Stiffeners. (47). The stiffeners must be proportioned ac¬ 
cording to specifications §§ 16 and 77. The end shear which 
must be transmitted by the end stiffeners to the abutment is 






i 


Art. 52. DECK PLATE GIRDER BRIDGE. 125 


377,500 ibs. To take this load we will need ._i_50%=72 

7876 1 ' 


rivets. (See Spec. § 56.) 

This number can be put into three pairs of stiffener angles 
with a single line of rivets in each angle. The stress, then, on 


each pair of angles will be, —— =125,800 lbs. The outstand- 

3 

ing legs of these end stiffeners must be as wide as the flange 
angles will allow, so we will try for these 2 Ls 7"x3%"x^". 


The allowed unit stress is 16000—70 —=15000 lbs per so. in. 

The required area of one pair of angles—=8.39 sq. in. 

15000 H 

We can, therefore, use for these stiffeners, 2 Ls 7"x3%"x i V / 
whose area is 8.82 sq. in. 

The minimum size of angles allowed for the intermediate 

120 

stiffeners is-[-2=6 inches for the outstanding leg. (See Spec. 

30 

§ 77). We will use for these 2 Ls 6"x3i4"x%". 

The spacing of the intermediate stiffeners must not exceed 
the distance “d” allowed by the formula in §77 of the specifi¬ 
cations. 


Required spacing at A=—( 12000 -—-—^=34 inches. 

40 \ 45 / 

Required spacing at ^12000 — 26 ^° Q ^=57 inches. 

. n 3 / 168000 \ . , 

Required spacing at 12000 — —— 77 inches. 

Required spacing at 12000 — ^=94 inches. 


Web Splices. (48). The total length of the girder is 103 ft. 
Plates 120 inches in width and only % inches thick are not listed 
in the Cambria hand book, but in the Carnegie shape book they 
are given and can be obtained up to 220 inches long, or 18'—4". 
It will therefore be necessary to splice the web at five points, 
making it in six pieces. The end sections may be made 18'—2" 
long and the intermediate sections each 16'—8". This will make 
the spacing of the cross frames uniform. 

The maximum bending moment at the first splice B, is as 
follows: 











126 


DECK PLATE GIRDER BRIDGE. 


Art 52. 


Dead Load— 686000 ft. lbs. 
Live Load =2236000 ft. lbs. 
Impact =1677000 ft. lbs. 

Total=4599000 ft. lbs. 


The actual flange area effective at this point is 35.84 sq. in., 
and therefore the bending moment taken by the web here is 

flo 

3 T8l X4,599,000=721,000 ft. lbs. At the splice this moment 
must be resisted by the splice plates FG, and the stress in these 

plates due to the moment will be —94,000 lbs. 

The maximum allowed unit stress on the extreme fiber of 
the girder is 16,000 lbs. per sq. in., and the maximum allowed 
unit stress on the splice plates FG will be proportional to their 
distances from the neutral axis of the girder, or. 


46 

60.6 


X 16,000=12,145 lbs. per sq. in. 


94000 

12145 


=7.73 


and the required area in the splice plates will be 
sq. in. 

This will require 2 plates 12"x 1 / 4" (net area=12.00—4X 


2 XlX 1 / 2 —'8.00 sq. in.). 



The number of 
rivets on each side of 
the splice in these 


plates will be 


94000 

7876 


= 12. 

The vertical 
splice plates to take 
the shear will require 


265100 

7876 


=34 rivets on 


each side. The de¬ 


sign shown in Fig. 48 
has 36 rivets on each 
side. 


These figures are 
for the splice at />, 
but usually the same 
design is used for all 
the splices. 


Fig. 48. 




































































Art. 52. 


DECK PLATE GIRDER BRIDGE. 


127 


It will be noted that the maximum shear and maximum 
moment have been used here as occurring simultaneously. This 
is on the side of safety, but a rigid solution would not give a 
splice appreciably smaller. 

A splice similar to the one shown in Fig. 40 may be used 
and calculated as follows. Here the number of rivets must first 
be assumed and then the stress in them calculated, to see that it 
does not exceed the allowed units. 

The splice, as drawn in Fig. 40, contains 52 rivets on each 


side, the vertical stress on each rivet, due to shear, is 


265100 

52 


5,100 lbs. The bending moment to be resisted by these rivets is 
721,000X12—8,652,000 inch pounds. The amount of stress 
on each rivet due to bending moment will be in direct propor¬ 
tion to its distance from the neutral axis. (12) 

Calling the stress on the outermost rivet *8, we have: 

46 x 49 

^XSO+i.S'X — X46+4SX —X42+. . .=8,652,000, or using 

50 50 

the letter y to represent the distance from the neutral axis to 
the rivet, in each case, we have r 1 


In this case 



4 A 


^\r=r-M 


50 

700 and S~- 


8652000X50 =9 248 ^ 
4X11700 


The resultant maximum stress on the outer rivet is 
j/ 5100 2 -f 9243 2 —10,560 lbs., which is in excess of the allowed 
’unit, (7876), and therefore the number of rivets would have to 
be increased if this type of splice were used in this girder. 

The splice plates must be strong enough, when considered 
as a beam 10314 inches deep, to carry the web’s proportion of 
the bending moment without exceeding a unit stress at the top 
and bottom, proportional to the distance from the neutral axis, 

or X 16,000=13,680 lbs. in this case. In figuring the mo- 
60.6 


ment of inertia of the plates, the rivet holes should be deducted. 


Lateral Bracing . 2 To provide for wind stresses and vibra- 


1 Strictly, these forces are perpendicular to lines drawn from the 
center of gravity of the entire group of rivets, to each rivet. 

2 See Heller’s “Stresses in Structures,” Chapter XIV. 










128 


DECK PLATE GIRDER BRIDGE. 


Art. 52. 


tions (See Spec. §10) a lateral system must be put in the span. 
Sometimes two systems are used, one in the plane of each flange, 
and sometimes only one is used, in the plane of the top flange, 
and the forces from the lower flange are transferred to the 
upper system by means of cross-frames (See Fig. 51) at inter¬ 
vals. Cross-frames are also put in to stiffen the bridge, when 
two systems of laterals are used. They are usually placed from 
15 to 20 feet apart, depending upon the width of the flanges 
of the girders. 

In a deck plate girder bridge, the lateral system is of the 
Warren, or sub-divided Warren type of truss with an even 
number of panels, so as to be symmetrical about the center line. 
The number of panels is so chosen that the laterals will be 
efficient, that is, so that they will not be inclined at too great 
an angle with the direction of the wind. Also, the panels must 
be short enough so that the actual unit stress in the top flange 
of the girder will not exceed that allowed by the specifications 
§28. 

The actual unit stress in the top flange is 13,700 

60.85 

lbs. per sq. in. Equating this to the unit as given in §28 and 

solving for l, we get 13,700=16,000—200 ^==16,000—107 from 
which 10/=2,300 and 7=230 inches=19'-2". 

The unsupported length of the top flange must not exceed 
this amount. 

We will divide the span into 12 panels, using a single 
system in the plane of the top flange, and put in cross frames 
at every second panel point. This will make a cross frame fall 
at each web splice. This is not necessary, but a stiffener must 
be at each cross frame. 

As but one system of laterals is to be used, it must be 
proportioned to carry the entire lateral force. 1 From the speci¬ 
fication §10 the load is 200+200+10% of 5000=900 lbs. per 
lineal foot of girder, and all of this is to be considered as a 
moving load. 


J For the calculation of the stresses in lateral systems of bridges 
having curved track see Heller’s “Stresses in Structures,” Art. 166, 
page 304. 




Art. 52. DECK PLATE GIRDER BRIDGE. 129 

The stresses in the laterals will be alternately compression 
and tension, and will all reverse when the direction of the wind 
reverses. Laterals, however, are never designed for reversals of 
stress, (See Spec. §20) so far as the reversal of the wind is 
concerned, because such reversals would occur only at long 
intervals. 

Since it requires more material to take care of the com¬ 
pression than the tension in a lateral, we are concerned only 
with the compressive stresses, and choose that direction of the 
wind which, for any particular lateral, will give compression 
in it. It will be assumed that the load is all applied at the 
windward panel points, although the live load is really applied 
at both girders. This assumption is on the safe side, and simpli¬ 
fies the calculation of stresses. 

On account of the cross frames, there are 12 panels on one 
side and six on the other. When the wind is blowing as indi¬ 
cated in Fig. 49, all of the panel loads will be equal and are 
16.67X900—15,000 lbs. each. This direction of the wind will 
give maximum compressive stresses in BC, DE, and FG, and 
these will be as follows: 



BC—-2y 2 X 15,000Xsec.#==54,100 lbs. 


DE= Xl5,000X«ec.ft=36.100 lbs - 

FG= f X 15,000X*«c.0=21,600 lbs. 



When the wind blows in the other direction as shown in 
Fig. 50, the compressive stresses will occur in AB, CD and EE. 
The panel loads on the lateral system for full loading are shown. 






















130 


DECK PLATE GIRDER BRIDGE. 


Art 52. 


AR—40,420 X$<30.0=58,500 lbs. 
671=27,430 X$ec.0=39,600 lbs. 
^=16,950X$oc.0=24,500 lbs. 


According to the specification §23, the unit stress for later¬ 
als may be increased 25% over that given for other members, 
and according to §72 the smallest angle allowed is 3%>"x3"x%". 
It is usual, where possible, to make laterals of single angles. 
The least radius of gyration of a single angle 3i4"x3"x%" is 
0.62". The unsupported length may be taken as the length 
between edges of flange angles, and in this case will be about 
11,55-1.55=10.0 ft.=120 inches. 

16,000—70 =2,450 lbs. per sq. in. Adding 25% gives 

3,060 lbs. per sq. in. This makes 1 L 3%>"x3"x%" worth 
2.30X3,060=7,040 lbs., which is far less than the least stress 
in the lateral system. 

Trying 1L 4"x4", the least radius of gyration is 0.79" and 
the allowed unit stress is 6710. The required area for 

21600 ' 

FG— -=3.22 sq. in. 

6710 

Use for FG 1 L4"x4"x ". Actual area=3.31 sq. in. 

Losing a 4"x4" angle for EF would require 24500 . —3.66 sq. 

6710 

in. This would require 1L4"x4"x 1 / 2 " which weighs more than 
1L5"x5"x%", so we will try 1L5"x5". The least radius of 
gyration=0.98" and the allowed unit stress in 9,300 lbs. per 

sq. in. The required area for EF— — 500 =2.64 sq. in. 

9300 

Use for EF !L5"x5"x%". Actual area=3.61 sq. in. 

Using a 5"x5" angle for DE requires —— .=3.89 sq. in. 

Use for DE !L5"x5"x p 6 Actual area=4.19 sq. in. 


Using 


a, 


5"x5" 


39600 


angle for CD requires*—- =4.26 sq. in., 


9300 


so 


we will try !X6"x6". The least radius of gyration is 1.18" and 
the allowed unit stress is 11,110 lbs. per sq. in. The required 

39R00 

area for CZ>=-^^-=3.56 sq. in. Use for CD lL6"6"x%". 


Actual area=4.36 sq. in. 








Art, 52. 


DECK PLATE GIRDER BRIDGE. 


131 


Required area for BC= 


54100 

11110 


=4.87 sq. in. Use for BC 


1 L6"x6' r x , t 6 Actual area=5.06 sq. in 

68500 


Required area for AB- 


11110 


=5.27 sq. in. Use for AB 


1 L6"x6"x%". Actual area=5.75 sq. in. 

The end cross frames must be proportioned to carry all the 
wind load to the abutment. It is usually considered that half 
of this goes through each diagonal to the supports, one diagonal 
being in tension and the other in compression. 

The total force acting at 
the top of the cross frame at 
A (See Fig. 49) is 43,300 lbs. 
12 8 



Sec.6— 


8 


Stress in top 


strut=21,700 lbs. 

S t r e s s in diagonal= 
21,7 OO*jc 0=34,6OO lbs. The 
diagonal in compression is 
supported at the middle in 
one direction by the tension 
diagonal, so an angle having 
unequal legs will be more 


economical than an equal legged angle for the diagonals. 
Try 1L6' / x3 1 / 4 ,/ x%". Allowed unit stress is 16000—70 


150 


1.94 


-|-25%=13,240 lbs. per sq. in. 

Required area= 3 ^ 6QQ =2.62 sq. in. Actual area^=3.43 sq. in. 

13240 

As this is larger than necessary we will try 1L5"x3 : 54"x%". 
The allowed unit stress is 11,800 lbs. per sq. in. Required area 

=2.93 sq. in. Actual area=3.05 sq. in. Use for diago- 

11800 

nals LL5"x3Vo"x 


// 


For the top strut try 1L3 %"x3 1 /2"x%' / . Allowed unit 

21700 

stress—9,000 lbs. per sq. in. Required area— ^ -—=2.41 sq. in. 

Actual area=2.49 sq. in. This is large enough so use for top 
and bottom struts 1Z3 1 / 4' / x3 1 /2 ,/ x%". 




















132 


DECK PLATE GIRDER BRIDGE. 


Art. 52. 


The amount of load transferred by the intermediate cross 
frames is only 3,333 lbs., so the smallest angle allowed by the 
specifications will be sufficient. Use for the intermediate cross 
f rames 3*4"x3"x%" angles. 

The number of rivets in the end connections of the lateral 
members is determined by the single shear value of a rivet. The 
laterals will be field riveted, so the value of a rivet will be 
6,013 lbs. 


AB requires 
BC requires 
CD requires 


58500 

6013 

54100 

6013 

39600 

6013 


=10 rivets. 
= 9 rivets. 


= 7 rivets. 


. 36100 . . , 

DE requires -=6 rivets. 

1 6013 

™ . 24500 r- • . 

EF requires - =5 rivets 

1 6013 

rr/. • 21600 . . , 

FC requires-=4 rivets. 

6013 


End cross frame diagonals require 
End cross frame struts require 


34600 

7216 

21700 


7216 


=5 rivets. 
=3 rivets. 


(Shop) 
(Shop) 


The intermediate cross frames will have to have all con¬ 
nections made with 3 rivets each, to comply with the specifica¬ 
tions §72. 

Shoes. The shoe should be of such design that it will dis¬ 
tribute the end reaction evenly over the masonry. For short 
spans it is customary to simply rivet a plate, not less than % 
inches thick, under the end of the girder, and allow this to rest 
on another similar plate resting on the masonry. With this 
form of shoe the load is applied heaviest at the inner edge of 
the masonry plate on account of the deflection of the girder. 
The best results are obtained, especially for long spans, by using 
hinged bolsters. (See Spec. §61.) 

The required bearing on the masonry (assuming sandstone) 


is 37 7 5 — =944 sq. in. (See Spec. §19). Using a shoe 3 ft. long, 

Q44 

it will require — =26.2 inches width. 

36 

The smallest rollers allowed are 6 inches in diameter 


(Spec. §58 and §60) and it will require 377500 =105 lineal 

3600 

inches of rollers under each bearing. (See Spec. §19). This 
will require five rollers each 21 inches long. 













Art. 52. 


DECK PLATE GIRDER BRIDGE. 


133 


The pin must be large enough to properly transmit the 

shear, and the required area is-^^—=15.7 sq. in. This re- 

2 X12000 

quires a pin 4% inches in diameter. 

The shoe must be strong enough to distribute the end reac¬ 
tion, as a beam, from the pin, evenly over the masonry, and 
must also be strong enough laterally to transmit the wind forces 
to the abutments. 

Fig. 52 shows a good design for the shoe. 

The estimate of weight can now be made upon forms as 
described in Art. 19, and if the actual dead load taken from 
the estimate does not differ enough from the assumed dead load 
to cause a. change in the size of any of the members, the stress 
sheet may be drawn, as shown in Fig. 53. • 



Fig. 52. 































































































































































































































































































































































































































































































































































Fig. 53. 














































































































Art. 53. 


THROUGH PLATE GIRDERS. 


137 


The difference in the actual dead load from that assumed 
is 1450—1367=83 lbs. per lin. foot. This would decrease the 

maximum moment 83 =103,800 ft. lbs., which would de¬ 
crease the required flange area at the center X 12 —0.66 

118.77X 16000 

sq. in., making the total required area 52.28—0.66=51.62 sq. in. 
If one of the cover plates be reduced in thickness ^ inches, the 
actual net area would be 51.59 sq. in., so therefore, the reduction 
in dead load would not allow a reduction in section of any 
member. 

The stress sheet will now be drawn up. (See Fig. 53.) 

53. Through Plate Girders. In a through plate girder 
bridge, all of the live and dead load, except the weight of the 
girders themselves, is concentrated at the panel points; and the 
weight of the girders may also be considered concentrated at the 
panel points to simplify the calculations. 

The shears and moments are found, then, as for a truss 
bridge. 1 

The flange diagram (similar to Fig. 47) will be polygonal, 
the area required at each panel point being calculated. 

The load on the masonry will equal the end shear of the 
girder plus the corresponding end reaction of the end floor 
beam (if an end beam is used). 

There is no vertical load on the flange rivets, and the pitch 
of the rivets will be constant between panel points because the 
shear is constant. 

There can be but one lateral system 2 , and this is made of 
the Pratt type with two diagonals in each panel. It is assumed 
that these diagonals take tensile stresses only; they are connected 
to the lower flanges of the stringers so as to take up the longitudi¬ 
nal force due to the application of the brakes on a moving train. 
This tractive stress would, otherwise, produce sidewise bending 
in the floor beams. 

The top flanges of the girders are supported at the panel 
points by means of solid web brackets extending down to the 

*See Heller’s “Stresses in Structures,” Chapters XII and XIII. 

2 See Heller’s “Stresses in Structurs,” Art. 151, page 275. 





138 


THROUGH PLATE GIRDERS. 


Art, 53. 


top of the. floor beams, and made as wide as the specified clear¬ 
ance will allow. 

Sometimes through plate girder bridges have solid floors, 
in which case the moment and shear vary as for a deck plate 
girder. 

In this case no lateral system would be necessary. 


CHAPTER VI. 

PIN CONNECTED BRIDGES. 


54. Construction. In a truss bridge, the loads are de¬ 
livered to the trusses at the panel points only. In the ordinary 
bridge this is done by means of floor beams and stringers. The 
stringers carry the ties and rails direct, and are in turn sup¬ 
ported by the floor beams at the panel points of the truss. This 
construction causes the moment in the truss to vary uniformly 
between panel points and the shear to be uniform in each panel. 
(53) 

55. Types of Trusses. Pin connected trusses are nearly 
always of the Pratt or Baltimore type, because the pin connec¬ 
tion is not well adapted to members whose stresses alternate in 
direction. 

The tendency is toward long panels, that is, ordinarily from 
20 ft. to 25 ft., because this gives few and heavy members both 
in the trusses and in the floor system, and these are cheaper to 
manufacture and give a stiffer structure under traffic. An odd 
number of panels is preferable to an even number, because the 
maximum moment will be less and because the structure may be 
made symmetrical about the center line with regard to field 
splices. 

The panel lengths must be chosen so as to give an efficient 
lateral system without increasing the width of the bridge be¬ 
yond that required for clearance of the roadway. For a single 
track bridge this width is usually about 16 ft,., depending, of 
course, on the width of the truss members. 

The economic depth 1 (46) cannot be determined with any 
degree of certainty, but is usually taken at from one-fifth to 
one-sixth of the length of span. The deeper the truss is made 
the stiffer it will be and the less the vibratory stresses will be. 
It is found that considerable variation in the depth will effect 
the weight and cost but little. The depth must be made suffi¬ 
cient to allow efficient overhead bracing without interfering 

1 See “Stresses in Bridge and Roof Trusses,” by W. H. Burr, Art. 
76, page 353. 

139 



140 


LOADS. 


Art. 56. 


with the clearances required by the traffic, unless a pony truss 
is used. 1 

Pin connected pony trusses are not desirable because of the 
lack of efficient transverse bracing. 

56. Loads. 2 Most specifications give a series of wheel 
loads representing the weights of two locomotives, followed by 
a uniform train load which is to be used in designing the struc¬ 
tures. In bridges over 100 ft. long, if an equivalent uniform 
load is used which will give the same center moment in the 
span, the errors in the stresses will not be large. It will be 
necessary to use several different equivalent loads for different 
parts of the structure, as, for instance, one for the stringers, one 
for the floor beams and hip verticals, and one for the trusses. 
The labor involved in obtaining these equivalent loadings for 
the floor beams and stringers is about as great as it is to calcu¬ 
late the stresses directly, so the wheel loads are generally used 
for these. 

An equivalent uniform load is usually used for the trusses 
(except the hip verticals). The stresses in some of the members 
will be too large and in some too small. The variation will 
usually be less than about 4% from the stresses obtained by 
using the actual wheel loads specified. 3 

Even if the exact loading specified should ever come upon 
the bridge, the stresses calculated from the wheel loads would 
not be the true stresses, because the track distributes the wheel 
loads differently from what we assume, and the stringers are 
partially continuous while we assume them to be simply sup¬ 
ported at each floor beam. Besides, the impact or vibratory 
stresses cannot be estimated with less than a probable error 
amounting to many times the discrepancy in the stresses ob¬ 
tained by the two methods. 

Numerous other methods of obtaining “equivalent” load¬ 
ings have been proposed, and it is probably due to the disagree- 


5 See Heller's “Stresses in Structures,’’ Art. 113 and 151. 

2 See Heller’s “Stresses in Structures,” Art. 119, 130 and 131. 

3 See Trans. Am. Soc. C. E., Vol. 42, pp. 189, 215 and 206. 

Also Johnson’s “Modern Framed Structures,” Chapter VI. 
Also DuBois’ “Stresses in Frames Structures.” 



Art. 57. 


TENSION MEMBERS. 


141 


meut on this point that engine loads are still specified in all but 
a few specifications, and that some engineers still calculate all 
stresses from wheel loads. 

The dead load must be estimated. The weight of the floor 
(52) including rails, ties and guards for the ordinary floor 
construction, with stringers not over 6 ft. 6 in. center to centei, 
will not exceed about 400 lbs. per linear foot of track. The 
weight of the steel work may be estimated approximately by 
comparison with some previously made estimates of similar 
structures, or may be taken from an empirical formula (52). 
After the design and estimate are completed, the dead load must 
be revised to agree with the final estimated weight, if the dis¬ 
crepancy is sufficient to change the size of any of the members. 
(51) (52). 

57. Tension Members. The tension members of pin con¬ 
nected trusses, except the hip verticals, and in some cases the 
counters and end panels of the lower chord, are usually made of 
eye bars. The counters and end panels of lower chord are fre¬ 
quently required to be made rigid members, to increase the 
stiffness of the bridge. The hip verticals should always be rigid 
members, because this gives a better connection for the floor 
beams at these points, and because it greatly reducs the vibra¬ 
tion. 

Eye bars are forged, and the heads are made of such size 
that in testing, the bar will break in the body instead of through 
the head. Usually the net section through the pin hole is made 
about 25% in excess of the section through the body of the bar. 1 

Eye bars should not be thinner than about % inch, and 
should not be too thick, say over about 2*4 inches. Thick bars 
will usually not show as high an ultimate strength as thin ones. 
The usual proportions of width to thickness lie between 3 to 1 
and 7 to 1. 

Built tension members, of course, contain more material 
than tension members of the same strength made of eye bars. 
The net section through rivet holes (111 and through the pin 
holes must be carefully investigated. The most common form 


3 Sizes of eye bars as manufactured by that company are given in 
Cambria, page 333. 



142 


COMPRESSION MEMBERS. 


Art. 58. 


is an I cross section made of four angles latticed together, al¬ 
though two channels latticed are frequently used. Sometimes 
two eye bars are laced together with bent bars, but this does not 
give a member much stiffer than the plain eyebar member. 

The required net area of a tension member is obtained by 
simply dividing the stress in the member by the allowed unit 
stress in tension as given by the specifications. 

58. Compression Members. The intermediate posts are 
usually made of two channels, either built or rolled, latticed 
together. Built channels are of course more expensive than 
rolled channels, on account of the extra punching and riveting. 

If the toes of the channels are turned in, the backs form 
plane surfaces to which connections may be more easily made 
than if the toes are turned out. The distance in the clear be¬ 
tween the channels must be great enough to allow the entrance 
of the riveting tool between the lacing bars, and it is economical 
to place the channels far enough apart to make the ratio of the 
unsupported length to the radius of gyration in the two direc¬ 
tions equal. 1 Local conditions frequently limit the dimensions 
of these members. 

Experiments show that a column will fail at an average 
unit stress over the entire cross section, which is less than the 
ultimate strength of the material in compression, and that the 
longer the column the less will be this average unit stress at 
failure. In other words, a column does not fail by compression 
alone but by a combination of compression and bending. 2 

This is taken into account in the design of compression 
members by the use of a “column formula," which gives us an 
average unit stress which it is safe to allow on the cross section, 
and after this unit is determined the design of the compression 
member is as simple as that of a tension member, but the deter¬ 
mination of the average unit stress allowable, involves properties 
of the cross section of the member, so the solution must be by 
trial. 


1 See Cambria, page 221. 

2 For an excellent article on Columns see editorial in Engineering 
News, January 3, 1907. 



Art. 58. COMPRESSION MEMBERS. 148 

A column formula consists of a variable reduction factor 

« 

applied to the maximum allowed fiber stress in compression. 

The column theory 1 assumes that the whole member acts 
as one piece, and the function of the stay plates and lacing is to 
hold the component parts of the member in line and to insure 
its action as a unit. 

A column under stress will deform into a curve with a point 
of contra-flexure near each end, 2 the distance from 
the end depending upon the degree of fixity of the 
end. At these points of contra-flexure the bending 
moment is zero, and consequently the stress on the 
column cross section is uniform. Midway between 
t hese points the maximum bending moment occurs, 
and the maximum unit stress in compression occurs 
on the concave side, therefore in a distance equal 
to one half the length between the points of contra- 
flexure, the unit stress in the concave side of the 
column'must change from the average to the maxi¬ 
mum allowed. 

Suppose a column to be made up of two leaves 
connected by lacing or otherwise. 

Let .sq=maximum allowed unit stress on the material 
in compression. 

P 

s .—average unit stress over the cross section— — 

A 

F 7 —total change in stress in one leaf of the column 
in a distance l. 

f =change in the total stress in one leaf per unit 

F 

of length=— 

/=the least distance from the point of maximum 
bending moment to a point of contra-flexure. 
L=total length of column. 

M 1 =area of cross section of one leaf. 

F=A, (si—s c ) 

. Aj (si—s/) 
l 


\r 



t P 
Fig. 64. 


1 See Seller’s “'Stresses in Structures,” Chapter X. 

2 See Heller’s “Stresses in Structures,” Fig. 137, page 178. 


( 16 ) 

(17) 










144 


COMPRESSION MEMBERS. 


Art. 58. 


For a pin ended column L=2l and for a square or fixed 
ended column L=4/. Any column in practice will lie somewhere 
between these two limits, and in any case eccentricities of manu¬ 
facture iand loading may make l different than theory would 
indicate. 

Also this theory assumes that the rate of change of stress 
in the leaf is uniform, which is not true, therefore, to be on the 
safe side we will take L—4/ in all cases; then 

4Ai(si— Sc) 


f~- 


( 18 ) 


Equation (18) gives the longitudinal increment of stress 
in one leaf per unit of length of column, and sufficient connec¬ 
tion must be provided between the leaves to transmit this stress 
(49). The values of s t and s c are taken from the column for¬ 
mula which is being used unless there is bending due to trans¬ 
verse loads. (77) 

When lacing 1 is used the bars must be capable of taking 
their stress either in tension or compression. 

The top chords and end posts are usually made of two built 
or rolled channels, connected by a cover plate on top and by stay 
plates and lacing on the bottom. The cover plate being solid 
aids in taking compression, and its area is always considered in 
the effective cross section. The cover plate then serves both as 
a part of the compression area and to tie the two leaves of the 
column together. 

A compression member with a cover plate on one side only 
is not symmetrical about its center of gravity, and the end 
connections must be designed to transmit the stresses to the cross 
section properly. (10) 

The cover plates should always be made as thin as the speci¬ 
fications will allow unless they have some special duty to per¬ 
forin, so as to keep the eccentricity of the section small. The 
unsupported width of plates in compression (distance between 
rivet heads) is usually limited by the specifications to 30 or 40 
.times the thickness of the metal. 

If a compression member is subjected to transverse loads. 


3 For various methods of calculating lacing see Report of the Royal 
Commission on the failure of the Quebec Bridge, Appendix No. 16. 
Also the Report of C. C. Schneider. 




Art. 58. 


COMPRESSION MEMBERS. 


146 


causing- bending 1 in addition to the direct load (40), the maxi¬ 
mum liber stress due to both must not exceed the maximum 
allowed unit compressive stress (s x ), and to be on the side of 
safety should not exceed a unit stress determined by a suitable 
column formula (s c ), because the accidental eccentricities may 
increase the bending due to the transverse loading. 

The horizontal and inclined compression members are in 
•bending due to their own weight in addition to being in com¬ 
pression. In the top chords and end posts of bridges this bend¬ 
ing moment is partially neutralized by lowering the centers of 
the end connections an amount sufficient to produce an upward 
bending moment due to the eccentricity of the compressive stress, 
equal to the downward bending moment due to weight. 


Pe= 


wL 2 

8 


and 


e= 


wlJ 

8jP 



Equation (19) is generally used in practice to determine 
the eccentricity of the pins to compensate for the bending due 
to the weight of the member. Using this value of e would render 
the bending moment almost zero at the middle, but as the bending 
moment (Pe) due to the eccentricity is a constant, while the 
moment due to the weight is a maximum at the middle and zero 
at the ends, the use of this value of e produces a negative bend¬ 
ing moment at the end as great as the original moment due to 
the weight. 1 It is better to use a smaller value of e as given by 
equation (20), 


e= 


wL 2 

10P 


( 20 ) 


as this Avill give a less resultant maximum bending moment in 
the column. 


Another case in which compression members are subjected 
to both axial and bending stresses is the end posts of a through 
bridge with overhead bracing. The end posts must carry the 
wind load in bending from the portal to the abutments. 2 This 
bending is in a plane perpendicular to that of the bending due 
to weight. The lacing and riveting of the cover plates of the 


1 See Heller’s “Stresses in Structures,” Art. Ill, page 190. 

VSee Article by Prof. J. E. Boyd in Engineering News for April 11, 
1907, page 404. 

2 See Heller’s “Stresses in Structures,” Arts. 153 to 105 inclusive. 





146 


LATERAL SYSTEMS. 


Art. 59. 


end posts must be sufficient to transfer the increments of stress 
as determined by equation (17). 

59. Lateral Systems. 1 In a through bridge a lateral sys¬ 
tem is always provided in the plane of the lower chord and, if 
the head room permits, in the plane of the upper chord also. In 
a deck truss bridge, lateral systems should always be provided 
in the plane of both the top and bottom chords. 

The top lateral system in a deck bridge and the bottom 
lateral system in a through bridge is assumed to take all the 
wind load on half the projection of the trusses, the floor system 
and the train and the centrifugal force if the track is on a 
curve, 2 although a small part of the latter would be transmitted 
to the top lateral system by the stiffness of the intermediate 
posts. 

The lateral system is a horizontal Pratt truss in which the 
door beams act as the posts and the chords of the main trusses 
act as chords. The diagonal members are put in in both direc¬ 
tions to provide for a reversal of wind. 

The top lateral system in a through bridge and the bottom 
lateral system in a deck bridge take the wind load on half the 
projection of the trusses. 

The end reaction of the top lateral system in a through 
bridge is conveyed to the abutment by means of portal bracing 
between the end posts and by bending in these end posts. 3 (58) 

Provision must be made in all main truss members carrying 
wind stresses for these, in addition to the dead and live load 
stresses. 

The wind blowing upon the side of a train on a bridge tends, 
to overturn it, and thus produces a greater load on the leeward 
truss than on the windward. The effect on the top chord of a 
through bridge is very small because the leeward top chord 
would be in tension under the wind load alone. The bottom 
chords and web members should, however, be proportioned for 
this additional stress. (63) 

60. Design of a Pin=connected Railway Bridge. To 

illustrate the methods of solving the various problems connected 

5 See Heller’s “Stresses in. Structures,’’ Chapter XIV. 

- See Heller’s “Stresses in Structures,” Art. 166. 

“‘See Heller’s “Stresses in Structures,” Arts. 153 to 165 inclusive. 



Art. 61. 


DEAD LOAD. 


147 


with the design of truss bridges, the design for a through Pratt 
truss railway bridge will now be worked out. 

We will assume the following data: 

Span 189 ft. c. to e. of end pins = 7 Panels at 27 ft. 

Single track. Alignment tangent. 

Specifications Cooper’s 1906 for Railway Bridges. 

Loading Cooper’s E 40. 

Material medium steel except rivets. 

61. Dead Load. (56) The stringers will be spaced 6 ft. 
6 in. c. to c., and the size of the tie mav be calculated as was 
done in Art. 52. We will use 8"x 8" ties 10 ft. long spaced 14 
in. c. to c., guard rails 6"x 8". The weight of the floor comes 
out somewhat less than 400 lbs. per lin. ft., but the specification 
§23 directs that not less than 400 lbs. per linear ft. shall be 
used. (51) 

The weight of the steel work may be approximately esti¬ 
mated from equation (15), w=7L-\~600 from which w=1923 
lbs. per lin. ft. of bridge. The total dead load then will be 
1923 4-400—2323 lbs. per lin. ft. of bridge, one-third of which 
will be considered as acting at the top chord and two thirds at 
the bottom chord. 

62. The Depth of the trusses (55) must be sufficient to 

allow the required head room 
and also an efficient portal. 
The depth of the floor system 
will govern this to some ex¬ 
tent also. 

An estimate of the depths 
required for these various 
parts may be made and an ap¬ 
proximate minimum allowed 
depth calculated in the form 
of a table similar to the one 
outlined in Art. 28. 

The stringer may be de¬ 
signed before this table is 
made up, as the depth of the 
truss does not effect it. We 
will use the stringer as de¬ 
signed in Art. 51, for this 
bridge. 

CD 



Fig. 55. 















148 


STRESSES. 


Art. 63. 


Depth of tie over stringer. 

... 0'-7%" 

(Spec. 

§12) 

Depth of stringer. 

... 4'-3i/ 4 " 



Bot. of stringer to bot. of FI. Bm. .. 

.. . 0'-6i/o" 




5'-5%" 



Bot. of FI. Bm. to Pin Cent. 

.. . 10V 4 



Base of Rail to Pin Cent. 

. . . 4'-7" 



Required Clearance . 

. . . 21'-0" 

(Spec. < 

§4) 

Portal depth say. 

4'-5" 

(min.) 


Total depth c. to c. of pins. 

. . . 30'-0" 

(min.) 



The depth should be about %• to % the span (55), so we 
will use a depth of 32'-0" c. to e. of pins. 


63. Stresses. For all of the truss members except the 
hip verticals, an equivalent uniform live load will be used, 



o - r/$. <56. 7<?/7. c 


Mem. 

/Deere/ 
Looe/ 
c 5/reuses 

L in?/ oac/v5 7reg2> e^> 

lV/nc/ <2>/rested 

72emerrA^s 

JEao/y 

i/n/form 

/7/ree/ 

Loo c/s 

Crorr? 

Lcr/2>US. 

/~7 0/77 
C7rorbf-/7/fi 

767o/ 
r /Vox- 

aS 

+723/00 

+235400 

+2/4x300 

3 

_ > 
+ 3/300 

+ 3/300 

Coo Cbr/o/ 

3c 

- 82/00 

-782400 

- /3O0OO 


± 22400 

- 22400 

4oo/ecfAT/ ttc/ 

Cc/ 

- 4/000 

-/2/600 

- 726/00 


1 4900 

- 74900 

zz 

// // 

■Oof 

- 0 

- 73000 

- 74000 


t 9 ooo 

- 9000 

// // 

Oc' 

+ 4/000 

- 36300 

- 34300 


t 4300 

- 4300 

'/ ✓✓ 

C'A 

+ 8Z/O0 

- /2/00 

- 9boo 


- 7300 

- 7300 

y/CTTo/ober 

36 

- 20900 


- 8O/00 


t 8000 

- gooo 

//Aq/ecf/y/oe/ 

Cc 

+ -4/800 

+ 93ooo 

+ 96900 


+ //400 

+ //400 

y ■ ■ 

/' & 

Oc/ 

+ 70300 

+ 03800 

+ 366007 


+ 6900 

+■ 6900 

// ✓/ 

ob 

- 79400 

-/6470O 

-/70600 

+ &/&?<? 

— O 

t 20200 

■+-~727g&c? 

~ 2OZ0O 

// // 

be 

- 79400 

-/6470O 

-/70600 

+/ 3 Sooo 
- S/6co 

t 20200 

+ 200 

-70/200 

//zoo/oxceecbjOL 

Cc/ 

-732300 

-274300 

-274300 

+ /S3200 
— 736000 

- 33700 

-769700 

r 

if *• f* 

e/Z 

- /S3800 

-329300 

-330/00 

t 763200 

t 40400 

-203600 

* // // 

3C 

+ /32300 

+274300 

+274300 

+■ /&/OO 

— 0 ' 

+ 33700 

+ 33700 

Aoq/ce/A/oc/ 

CO 

+ /388O0 

+329300 

+330/00 

+ Z7ZOO 
- /fi/00 

+ 21-0400 

+ 27200 

// A 

OD 

+ 708800 

+ 329300 

+-330/00 

+27200 

+ 40400 

+27200 

// // 


derived from the maximum live load moment for the span. (56) 
This equivalent uniform load for a 189 ft. span is 4820 lbs. per 
lin. ft. of track. 














































































Art. 68. STRESSES. 149 

Panel load of Dead Load= 2323 X 2 ^ 31 36Q lbs< 

2 

Panel load of Live Load— ^ 82Q ^ 2 ' =65,070 lbs. 

2 

The table under Fig*. 56 gives the direct stresses in all of 
the truss members due to dead load, live load, and wind. The 
live load stresses calculated from the wheel loads are also given 
in a parallel column for comparison. The maximum error is 
seen to be in the end posts and amounts to about 3%%. 

The wind stresses in the chords from the lateral systems are 
aotten bv assuming* that the trusses are 16'-0" c. to c. This 

will not be far 
from right. 

According to 
specifications, §24, 
450 lbs. of the 
wind load shall be 
treated as acting 
on a moving train 
at a height of six 
feet above the base 
of rail. This gives 
a height of 6.0+ 
4.58 = 10.58 • feet 
above the pin cen¬ 
ters. The hori¬ 
zontal force acting 
at this height (see 
Fig. 57) will be 
450X 27 = 12,100 
lbs. per panel. The 
additional load on 
the leeward truss at each panel due to this overturning moment 
will be 

V=’ 12100 X 10 - 6 J =8,000 lbs. 

16 

The additional stress in each member then will be the direct 
live load stress in the member, (figured for the equivalent uni- 

8000 



form load) multiplied by 


65070 






































160 


DESIGN OF TENSION MEMBERS. 


Art. 64. 


The specifications §39 directs that the stresses in the truss 
members due to wind may be neglected unless they exceed 30% 
of the combined dead and live load stresses. Therefore we will 
have to consider the wind stresses only in the bottom chords. 
The bending in the end posts due to the portal stresses will be 
taken up in Art. 66. 


64. Design of Tension Members. The required net area 
for any tension member is obtained by adding algebraically, the 
areas required for dead load and live load stresses. (Spec. §31 
and 35). There is also a limiting clause for counters. (Spec. 
§50 and 51.) 

Since in these specificfiations, the dead load unit stress is 
just twice the live load unit, the same area will be obtained if 
the live load stress plus half the dead load stress be divided by 
the live load unit stress. 

From this relation we may derive an average unit stress 

which may be applied to the total dead plus live load stress in 

any member as follows: 

•/ 

Let s /K ==this average unit stress. 

the dead load unit stress. 

<<q=the live load unit stress. 

D—the dead load stress in the member. 

L —the live load stress in the member. 

Then 


D-\-L 2 (D+L)s, 

—: S ir 


2 s, 


s 


IV 


D+ 2L 


i-t- 


D+L 


s D —2 Sjr s a 


>Z) 


H 


( 21 ) 


D+L 


It is not necessary to find this average unit stress except 
for those members in which the wind stress must be taken into 
account according to specifications §39. 


The simplest members, those made up of eye bars, will be 
proportioned first. We will assume that we are limited in the 
choice of eye bars to those manufactured by the Cambria Com¬ 
pany, as indicated in their hand book, pages 332 and 333. 









Art. 64. 


DESIGN OF TENSION MEMBERS. 


151 


Be Required D. L. Area= — —- =4.11 sq. in. 

20000 

Required L. L. Area= - 1 — =18.24 sq. in. 

10000 _ 

Total=22.35 sq. in. 

This may be'made up of 4 bars 6"x} j? " (area=22.50 sq. in A 
or 2 bars 7"xl%" (area=22.76 sq. in.). The 6 inch bars are 
slightly more economical and will not require such large heads 
so we will use 4 bars 6"x+J" for Be. 

Cd Required 1). L. Area— =2.05 sq. in. 

20000 

o i T -p \ 121600 10 

Required L. L. Area= - =12.16 sq. m. 

10000 - 

Total=14.21 sq. in. 

This will require 2 bars 6"xl 1 3 6 " ^»rea=14.25 sq. in.) 

Dd' Required D. Ij. Area=00 

r> • -i |- T * 78000 _ 0 

Required L. L. Area= - =/.3 sq. in. 

10000 

This will require 2 bars 4"x]|" (area=7.50 sq. in.) or 

2 bars 3"xli4" (area=7.50 sq. in.). The 3 inch bars cannot be 
used because, probably the size of the pin at d will exceed 5 in., 
which is the largest size that the table in Cambria gives for a 

3 inch bar, so we will use 2 bars 4"x]f" 

An increase in live load of 25% or to E50, will increase the 
unit stress in this counter exactly 25% so §51 of the specifica¬ 
tions is satisfied. 


D'c' 


Required D. L. Area= 
Required L. L. Area= 


41000 

20000 

36500 

10000 


=2.05 sq. in. 
=3.65 sq. in. 


Difference=l. 60 sq. in. 

To comply with specifications §51 an increase in live load 
of 25% must not increase the unit stresses more than 25% 
therefore: 


Required D. L. 
Required L. L. 


A rea= 


Area= 


41000 

20000+ 25% 
36500 + 25 <f 0 
10000 + 25% 

Difference 


=1.64 sq. in. 

=3.65 sq. in. 
=2.01 sq. in 












162 


DESIGN OF TENSION MEMBERS. 


Art. 64. 


This will require 1 bar 1 ^ in. square* (area=2.07 sq. in.). 

cd . The average unit stress allowable, as determined by 
equation (21) must be used here because the wind stress is more 
than 30% of the dead and live load stresses. (Spec. §39.) 

20000 

s w — 274 5 _ ~11,940 lbs. per sq. in. 

1+ 406.8 

ll,940-f-30%=15,520 lbs. per sq. in. 

Total stress in cd=132.3+274.5+169.7=576.5. 

Required Area= 5765 —=37.14 sq. in. 

15520 

This will require 4 bars 6"xl(area=37.50 sq. in.) or 
2 bars 7"xl +/' plus 2 bars 7"xl%" (area=37.64 sq. in.) 

The 7 inch bars will be better 'because the thickness is less, 
and this will give a less bending moment on the pin, and also 
probably the next chord eld' will necessarily be made of 7 inch 
bars, in which case the same dies may be used for making all 
of the eye bar heads in the bottom chords, which would reduce 
the cost. 

dd' Total stress=158.8+329.5+203.6=691.9 

Allowed unit stress=15,520 lbs. per sq. in. 

d • i a 691900 . . _o 

Required Area=-r=44.58 sq. m. 

16620 H 

This will require 2 bars 7"xl%" plus 2 bars 7"xl t 9 6 " (area 
=44.64 sq. in.). 

According to the specifications §10 the vertical suspenders 
and the two end panels of lower chord must be made rigid 
members. 

abc Total stress=79.4+164.7+101.8=345.9 

Allowed unit stress=15,520 lbs. per sq. in. 

r , • i a 345900 

Required Area=-=22.29 sq. m 

15520 1 

This member may be made up of 4 angles 
and 2 plates laced together horizontally as 
shown in Fig. 58. We will use 4 angles 
O^xS^+'x+Z', and 2 plates 14 inches wide by 
as thick as may be necessary to make up the 
required net area. To comply with specifica¬ 
tions §64 at least two rivet holes must be 
deducted from each angle. (11) 


i 






i 


Fig. 58. 















Art. 64. 


DESIGN OF TENSION MEMBERS. 


153 


Net area 4 angles 6"x3%"x%" = 18.00 — 8xlx% = 14.00 
sq. in. 

Required net area of plates—22.29—14.00=8.29 sq. in. 

Equivalent net width of plates=14—2x1=12 inches. 

Required thickness of plates=-^-=0.69 inches. 

Use 2 plates 14"x%". Total actual net area 

2 Angles 6 / 'x3% // x 1 / ‘2' / =14.00 sq. in. net 
2 Plates 14"x%"= 9.00 sq. in. net 

Total=23.00 sq. in. net 

It would be more economical to use four angles without 
cover plates, but it is not well to use metal thicker than about 
% inch in a riveted tension member, besides, according to 
specifications §129, material over % inch in thickness in tension 
members must be reamed, which would increase the cost con¬ 
siderable. 

*/ 

Bb will be made of two rolled channels, and will be made 
the same width as the intermediate posts Cc and Dd so that the 
floor beams may all be made alike. 

The allowed unit stresses are less for verticals carrying 
floor beams than for other truss members (Spec. §31). 

. , -p. T \ 20900 1 01 

Required D. L. Area=-= 1.31 sq. m. 

1 16000 1 

Required L. L. Area= =10.01 sq. in. 

1 8000 T _ 1 

Total=11.32 sq. in. 

There will be pin plates on the webs of the channels for 
the connection at B , and stay plates riveted to the flanges near 
them. These will make it necessary to take at least 4 holes out 
of each channel as shown in Fig. 59. 

The member cannot be made of less than 10 inch channels 

i 

or there would not be room for the floor beam 
connection. The lightest weight 10 inch channel 
cannot be used because specifications §82 re¬ 
quires that no metal less than % inches thick 
be used, and the web of a 10" by 15 lb. channel 
is only 0.24" thick. 


r i 
lj 

Fig. 59. 












154 


DESIGN OF COMPRESSION MEMBERS. 


Art. 65. 


2 —10"X20 lb. channels is about the smallest section that can be 
used. 

The rivets in the flanges cannot be larger than (see 

Cambria, page 53), while it is desirable to have the rivets in the 
web for the floor beam connections. 

The net area then of the 2 channels 10"x20 lb.=11.76— 
4x i T g-4x0.38x1—8.71 sq. in. As this is less than the 
required area we must use heavier channels. Try 2 channels 
12"x25 lbs. Net area=14.70—4xi/>x%—4x0.39x1=11.39 sq. in. 
These will answer. 

65. Design of Compression Members. The least allowable 
section for a post is 2 channels 10"x20 lbs. (See Spec. §§35 and 
82.) The greatest allowed length for a post composed of these 
channels is 100 times the radius of gyration (Spec. §35) = 
100X3.66=366 inches=30' — 6", which is less than the depth of 
our truss, so a larger section must be used. Try 2 channels 
12"x25 lbs. Allowed length=100X4.43=443"=36'—11". 

Allowed unit stress for D. L.=17000 — 90— 

r 


17AAA 90X32X12 nr»A a n 

=17000-—-=9200 lbs. per sq. m. 

4.43 


Allowed unit stress for L. L.= 4600 lbs. per sq. in. 


Del Required D. L. Area^= 1Qo() Q ___ ^ 14 sq. in. 

9200 1 

Required L. L. Area= 66800 —12.13 sq. in. 

Total=13.2? sq. in. 

Actual area=2X7.35=14.70 sq. in. which is sufficient. 

Cc. The stresses for this post are considerably greater than 
for Dd, so we will try 2 channels 15"x33 lbs. 

Allowed D. L. unit stress=10,850 lbs. per sq. in. 
Allowed L. L. unit stress= 5,420 lbs. per sq. in. 

Required D. L. Area= j 1800 — 3.86 sq. in. 

10850 1 

Required L. L. Area= - 93Q °° =17.16 sq. in. 

52400 _ 


Total=21.02 sq. in. 

Actual area 2 channels 15"x33 lbs.=2X9.90=19.80 sq. in. 
Try 2 channels 15"x40 lbs. 










Art. 65. 


DESIGN OF COMPRESSION MEMBERS. 


156 


Allowed D. L. unit stress=10,650 lbs. per sq. in. 
Allowed L. L. unit stress= 5,320 lbs. per sq. in. 

Required D. L. Area= — 3 93 sq. in. 

10650 


Required L. L. Area= 


93000 

5320 


=17.48 sq. in. 


Total=21.41 sq. in. 

Actual area 2 channels 15"x40 lbs.=2X 11.76=23.52 sq. in., 
which is sufficient. 

In the above calculations for the posts we have assumed 
that the ratio of unsupported length to radius of gyration in 
the direction parallel to the webs of the channels was greater 
than that in the other direction (58). In order to make the 
posts safe according to the specifications, the distance between 
channels must be sufficient so that the allowed unit stress is 
greater than the actual. 

134800 


The actual unit stress on Cc= 


23.52 


=5730 lbs. per sq. in. 


From equation (21) the allowed unit stress 

L- 


=[ 


17000—90 


r 


k 134 8 / 


=10060—53.25 —^ 


r 


Equating these two units we get 

5730=10060—53.25 —from which r=3.1 in. 

r 

This is assuming that the post is supported by sway bracing 
at an elevation of 21 ft. above the floor beam. (Spec. §107). 

The distance apart of the channels necessary to make the 
radius of gyration equal to 3.1 in. will now be calculated. 

I—I -I -Ad 2 in which 

o I 


V4 


l =moment of inertia of channels about their own center 

O 

of gravity. 

d=distance from the center of gravity of the column to the 
center of gravity of the channel. 


2X9-39+2X11.76Xri 2 0 1 » , 

— - ' ,, - - =3.1 from which 

1 2X11.76 


\ 

cZ-=8.81 d— 2.97 inches 

The minimum distance back to back of channels (toes turned 














166 . 


DESIGN OF COMPRESSION MEMBERS. 


Art. 66. 


in) then will be 2X2.97-{-2X0-78—7.5 inches, but Spec. §35 
says that the least width of post permissable is 10 inches, so we 
will use this width. 

The post Del will be made the same distance back to back 
in order that the floor beams may be made alike. 

The width of the top chord and. end posts must be made 
the same throughout, and the depth of the two are usually made 
the same, although this is not absolutely necessary. 

The width must be sufficient to allow all of the web members 
to connect to the pins inside of the top chord section. In some 
cases a pair of eye bars are allowed to connect to the pin outside 
the chord section, but this is unusual. 

There are more members connecting* at B than at any other 
point, so the required width there will be determined. 

We can only estimate this width approximately at present. 

♦ 

Width of Bh back to back or channels= 10" 

Pin plates on Bb say 2— y 2 " = 1" 

Bars Be 2—-J-J" (2 inside Bb) =1%" 

Webs of end posts say 2 —%" =\i/ 2 " 

Pin plates on end posts say 2— y 2 f = 1" 

Top angles on end posts say 2 — 3" = 6" 

Clearances say 1%" 

Total=22i/ 2 " 

In order to make sure that we have sufficient clearance we 
will make the cover plate of the chord 24 inches wflde. 

The depth of the chord section must be made sufficient so 
that there is room between the pin and the cover plate for the 
connection of the members. The pin will be somewhat above 
the geometric center of the web plates because the center of 
gravity of the section will be above the center of the web. 

• 4 * 

Assuming this eccentricity of the pin to be 1 y 2 " and that 
the radius of the largest eye bar head is not over 7%", we have 
9" as the half depth of the web required by the clearances. 

Figure 60 shows about the dimensions of the minimum 
chord section which we can use here. 




Art. 65. 


DESIGN OF COMPRESSION MEMBERS. 


157 


The specification §80 



requires that the thickness of plates 
in compression shall not be less than 
gV of the unsupported width, except 
for the cover plates of top chords and 
end posts which are limited to 
The unsupported width of the plate 
is the distance between rivet heads. 
For the cover plate it will be (1) 
21i4"-l 1 V'=19 1 1 |". The minimum 
allowed thickness of cover plate then 


will be 
will be 


19.8 

40 

13.3 

30 


=%". The minimum allowed thickness of web plate 
=0.45" or say also. 


For the chord sections CD and DD we will try the following:, 
which is about the least chord section allowable as we have seen. 
2 Web plates ^18-00 sq. in. 

1 Cover plate 24 "XMj”—■ 12.00 sq. in. 

2 Top angles 3"X3"X%"— 4.22 sq. in. 

2 Bot. angles 4"X3"X%' / = 4.98 sq. in. 


Total=39.20 sq. in. 

We will now find the location of the center of gravity of the 
cross section by taking moments of areas about the upper side 
of the cover plate (see Fig. 60). 

Cover plate 12X 0.25= 3.00 
Top angles 4.22X 1.39= 5.86 
Web Plates 18.00X 9.62=173.25 
Bot. Angles 4.98X17.97= 89.49 


Sum=271.60 

Distance of center of gravity from top of cover plate 

271.60 a OQ . 1 

==-=6.93 inches. 

39.20 

The distance of the center of gravity above the center of the 
web plate=9.63—6.93=2.7 inches. 

The least radius of gyration is required to be used in the 
determination of the allowed unit stresses. This will be about a 
horizontal axis through the center of gravity, and is equal to 


1 































158 


DESIGN OF COMPRESSION MEMBERS. 


Art. 65. 


r 

The moment of inertia about this axis must now be found. 1 
This is done by adding to the moment of inertia of each con- 
stituent part the product of its area by the distance squared, of 
its center of gravity from the center of gravity of the section. 

Cover p late 0.25 

12 

12.00X (0.68)-= 535.47 
Top angles 2x1.76= 3.52 

4.22X (5.54) 2 = 129.52 

Web plates- X ^ x(18)3 = 486.00 

12 

18.00X (2.70) 2 = 131.22 
Hot. angles 2X1-92= 3.84 

4.98X (11.04) 2 = 606.97 


Total Moment of Inertia=1896.79 

From which we get the radius of gyration about the hori- 

* * 

zontal axis through the center of gravity 


1 

\~A 


1896.79 

89.20 


=6.95 inches. 


L 


The allowed dead load unit stress is 20000—90—=15,800 

r 

from specifications §35. 


L. 

Area= 

158800 



15800 

L. 

Area= 

329600 



7900 


=10.05 sq. in. 

=41.71 sq. in. 

Total=51.76 so. in. 

A 

llie area of cross section must therefore be increased. AVe 
will try the following: 

2 Web plates 18"X%"=27.00 sq. in. 

1 Cover plate 24 /, X ] /o // =i2.00 sq. in. 

2 Top angles 3"X3"XiV'= 4.88 sq. in. 

2 Bot. angles 4"X3"X%"= 7.98 sq. in. 


Total=51.86 sq. in. 

Eccentricity=l.68 in. 7=2494 >=6.93 in. 

llie change in the radius of gyration is seen to be very small, 


1 See Heller’s “-Stresses in Structures,” Art. 67, page 92. 















Art, 66. 


DESIGN OF THE END POSTS 


159 


and the corresponding change in the allowed unit will be very 
small, so this section will answer. 

BC. The section for this chord will lie somewhere between 
the two tried above, and therefore we may use the same allowed 
unit stresses. 

»j> • i i\ i \ _ 132300 o oq 

Reci in red D. L. A rea=-= 8.38 so. m. 

15800 

t, ‘ITT \ _ 2 ( 4o00 O/i nr 

Required L. L. Area=-=34. io sq. m. 

7900 _ 

Total—43.13 sq. in. 

Use the following section 

2 Web plates 18"X 1 9 6 "=20.25 sq. in. 

1 Cover plate 24"XM*”—12.00 sep in. 

2 Top angles 3"X3"X%"= 4.22 sq. in. 

2 Bottom angles 4"X3"XiV ,= 7.26 sq. in. 

Total==43.73 sq. in. 

Eccentricitv=1.98 in. /=2230 >-=7.14 in. 

66. Design of the End Posts. Before the end posts can 
be designed the stresses in them due to the portal bracing must 
be determined. 














160 


DESIGN OF THE END POSTS. 


Art. 66. 


From Fig. 55 we see that we can make the vertical distance 
from the upper clearance line to the upper pin center 6 ft. 5 
inches. 

Fig. 61 illustrates the method of determining the depth of 
portal which we may use. This may be laid out to scale and the 
depth scaled. For the purpose of calculating the stresses the 
depth does not have to be determined closer than the nearest 
0.1 ft. 

In the following calculations of the stresses in the end posts 
and portal bracing due to wind, the methods and notation used 

in Heller’s “Stresses in Structures 
Arts. 153 to 165 inclusive, will be fol¬ 
lowed. The specifications §106 directs 
that the portals be latticed and that 
they be connected rigidly to the end 
posts and top chords. 

Fig. 62 gives the general dimen¬ 
sions of the portal bracing and end 
posts. 

First, it must be determined 
whether the end posts are fixed at the 
ends by the direct stresses, or not. 

From Fig. 60 we may determine 
approximately that 

7^—fc 2 =about 17 inches. 

P =Panel load of wind load on 
top lateral system=200X27=5400 
pounds. 

7?=Reaction of top lateral system on the portal=2 P (there 
are 5 panels in the top lateral system.) =10,800 lbs. 

To test for the degree of fixity of the ends of the posts as¬ 
sume 11=I I / = 1 / 4 (R -j- P ). (This is assuming fixed ends.) Then 
H=IP=8,100 lbs. 

The portal being rigidly connected to the end posts from 
B to F, fixes the tops of the posts, then the point of contra- 
flexure would occur midway between a and F or x 1 =x 1 '=17.0 ft. 

M 2 =Hx t =S 100X17=137,700 ft. lbs.=l,652,400 in. lbs. 
With moments about a point of contra-flexure we get, 



















Art. 60. 


DESIGN OF THE END POSTS. 


161 


V=—V'=\- (R+P) (a+d-x i)=— —x 16200 x (43.0-17.0) 
b 16.16 

=26,100 lbs. 

The maximum stress in the end posts occurs in the leeward 
post when the live load is on the bridge and when the wind is 
acting. 

Dead Load stress =123,100 lbs. 

Live Load stress =255,400 lbs. 

Overturning tendency due to wind on train= 31,300 lbs. 

V due to wind on top lateral system = 26,100 lbs. 

Total maximum direct stress =435,900 lbs. 

The concurrent direct stress in the windward post will be 
123,100+255,400—31,300—26,100=321,100 lbs. 

The moment of the direct stress at the bottom of the wind¬ 
ward post tending to fix the end is 

+++>=321,100 X%X 17=2,729,400 in. lbs. 

As this is greater than the moment M. 2 tending to rotate the 
post at er, the posts will be fixed at the bottoms. 

The maximum bending moment in the post occurs either at 
a' or at F\ and is 1,652,400 in. lbs. 

We will try for the end posts the same section as was used 
for top chord sections CD and DD. 

The moment of inertia must be calculated for a vertical 
axis through the center of gravity. 

Area of cross section=51.86 sq. in. Eccentricity=1.68 in. 

I (horizontal axis)= 2494 r (horizontal axis)=6.93 

I (vertical axis) =3848 

The average allowed unit stress for dead and live loads 
from equation (21) 

L 

17000-90— 

s w =_ — — -=6245 lbs. per sq. in. 

256400 L675 

1-f-• 

378500 

When wind stresses are added to the dead and live load 
stresses this unit may be increased 30%, (Spec. §39), making 
it 8120 lbs. per sq. in. 

For this cross section the actual maximum fiber stress 
would be (58) 










162 


DFSIGN OF THE END POSTS. 


Art. 66. 


P , Me 435900 , 1652400X12.875 

«Srr»ay" ■ ■ ■ . 1 I “ 

A I 51.86 ' 3848 

=8405+5528=13933 3bs. per sq. in. 

Therefore the section must be increased. 

As the moment of inertia increases when the area is in¬ 
creased, we may arrive at an approximate figure for the area by 
considering the equation above as follows: 

8405 : s w =13933 : 8120 from which s w =4900 lbs. 

This value of s w assumes that in changing the section we 
have not changed the radius of gyration, and of course can be 
used only as a general guide. 

Using this value of s w we find that the approximate required 

area will be-=89 sq. m. about. 

4900 1 

It will be found by trial that this area cannot be made up 
without materially reducing the radius of gyration, and conse¬ 
quently the allowed unit stress, unless the width or depth of the 
section be increased. 


If the width were incresaed it would necessitate an equal 
increase in width of the top chord sections and add materially 
to their weight without increasing their efficiency. (See Spec. 
§§80 and 100), but the depth of the end posts may be increased 
somewhat without changing any of the top chord sizes. 

After several trials the following section was chosen : 

1 Cover plate 24"X%"=15.00 sq. in. 

2 Web plates 21"X 7 / 8 "=36.75 sq. in. 

2 Top angles 3"X3"X%"= 6.72 sq. in. 

4"X3"X%"= 7.98 sq. in. 

15"X%' /= ==18.75 sq. in. 

Total=85.20 sq. in. 

The properties of this section are as follows: 
Eccentricity=1.77 in. Area=85.20 sq. in. 

I (horizontal axis)=4698 / (vertical axis)=6424 

r (horizontal axis)=7.43 in. 


2 Bot. angles 
2 Side plates 


Allowed D. L. unit stress=17000—90-=10913 lbs. persq. in. 

r 

Allowed unit stress for I). L.+L. L. from Eq. (21)= 6516 
lbs. per sq. in. 






Art. 67. 


THE PORTAL BRACING. 


163 


Allowed unit stress for D. L. +L. L.-fWind=8468 lbs. per 
sq. in. 

™ , 435900 , 1652400X12.875 

Max. extreme fiber stress=- -L-—- 

;85.20 ' 6424 

=5116-)- 3312=8428 lbs. per sq. in, 
67. The Portal Bracing. The maximum stresses in the 
portal bracing will occur when there is no live load on the 
bridge. 

The direct stress then in the leeward post, assuming fixed 
ends as above, is as follows: 

Dead Load stress=123,100 lbs. 

V= 26,100 lbs. 


Total=149,200 lbs. 

The concurrent direct stress in the windward post=123,100 
-26,100=97,000 lbs. 


The moment of the direct stress at the bottom of the leeward 
post tending to fix that end is 

1 /2^ 2 Z)=149,200X V'2 X 17=1,268,200 in. lbs. 

The moment M 2 required to fix that end is 1,652,400 in. lbs., 
therefore the posts are only partially fixed at the bottoms, the 
tops are fixed by the construction. An approximate mean value 
of x x and x\ may be gotten from the equation 

4&2D 

x m = —-- 

i(R+P) 

Neglecting V in the value of I) we get 


x 


8.5 X 123100 


rrr 


8100 


=129 in.=10.75 ft. 


We may now get an approximate value for V. 

1st Approx.F=— V'=— (K+P) (a-\-d— x m ) 

b 

= —— V16,200(43-10.75) =32,300 lbs. 

16.16 

2nd Approx, D =123,100—32,300= 90,800 lbs. 

2nd Approx. D' =123,100—f-32,300=155,400 lbs. 

2nd Approx. M 2 =8.5X 90,800= 771,800 in. lbs. 

2nd Approx. M 2 =8.5Xl^fi>400=l,320,900 in. lbs. 

2nd Approx. E ' ] 














164 


THE PORTAL BRACING 


Art. 67. 


=% (16,200-, 

2X34X12 

2nd Approx. H ~R-\~P — H'= 7090 lbs. 

OJA My 771800 

2nd Approx. x x ———= 


X549,100) =9110 lbs. 


2nd Approx. x\ 


H 

My' 


7090 
1320900 


H' 


9110 


109 in.= 9.08 ft. 
145 in.=12.08 ft. 


1 


2nd Approx. V=-V'= — [ ( H+P) (a+d-x, ) -H'(x\-x x ) ] 

b 

16,200(43—9.08)—9,110X3]=32,330 lbs. 


16.15 


As this value of V does not differ materially from the first 
approximation the values of the other quantities are also deter¬ 
mined closely enough. 

Taking a section Im through the portal and a center of 
moments at the bottom flange 


Stress in top fiange=77-|- 1 /2-f >- b^ 


a — x\ 
~cT 


x 

~d 


=10800+2700+7090 -?? 1 ??—32 330 JL 

9.0 ’9 

The maximum compression in the top flange then will occur 
where x=0 and the maximum tension where x=b. 

Max. Comp, in top flange=33,100 lbs. ( + ) 

Max. Tens, in top flange=24,900 lbs. ( —) 

Taking the same section and a center of moments in the 
top flange 

Stress in bottom flange of portal=?Z —— _ V — 

d d 

The maximum tension occurs where x=0 and the maximum 
compression where x=b. 

QQ Q9 

Max. Tens, in Bot. Flange=7090— : —=26,700 lbs. (—) 

9 


Max. Comp, in Bot. Fiange=26700—32330 — - 5 =31,300 

9 

lbs. (-]-) 

The maximum shear at any section is F=32,330 lbs. 

For the portal flanges the least allowable radius of gyration 


is 


X 14X12=1.4 inches. (Spec. §35). 


120 


















Art. 68. 


DESIGN OF FLOOR BEAMS. 


165 


This radius of gyration is taken perpendicular to the plane 
of the portal. 

Try 2 Angles 5"x3"x , 5 inch legs outstanding. 

Area—2X2.41=4.82 sq. in. gross. r=2.47 in. 

The allowed unit stress=13,000—60——8920 lbs. per sq. in. 

r 

i 3 3100 0 

Reqd. area= --=3. 1 1 sq. m. 

8920 

These are large enough for the maximum compression 
stress. 

26700 

The required net area for tension=-=1.48 sq. in. 

18000 1 

Actual net area=4.82—2X fVX 1=4.20 sq. in. (%" Rivets.) 
For the lattice of the portals we will use angles spaced about 
as shown in Fig. 62. 

Any vertical section will cut four lattice angles, so we will 
consider the shear as equally divided among them. 

The secant of the angle of inclination of the lattice is about 

1.4, so the stress in each lattice angle=1.4X—— =11,300 lbs. 

4 

tension or compression. 

The smallest angles allowable to use are 3 "x2%"x-jV', (See 
Spec. §83), which will be ample to take the above stress. 

68. Design of Floor Beams. The weight of the beam itself 
is a uniform load, the weights of the floor, stringers and live 
load form two concentrated loads on the floor beam 6'-6" apart. 
Since the beam’s own weight is a very small proportion of the 
total load, it will be considered as concentrated at the stringer 
connections also. 

The miaximum live load concentration on the beam may be 
taken from the specifications, Table I, or calculated from the 
wheel loads. 

Live load at each stringer eonnection=80,000 lbs. 

Dead load from floor =200X27= 5,400 lbs. 

Weight of stringers =165X27= 4,455 lbs. 

Weight of 5% ft. of floor beam say = 945 lbs. 


at each stringer. 


Total Dead Load=10,800 lbs. 








166 


DESIGN OF FLOOR BEAMS. 


Art, 68. 


t 

The distance center to center of trusses is 16 ft. 1% in. 
This is considered as the distance between supports of the floor 
beams. The distance between the center of the truss and the 
nearest stringer connection is 4'-9%". 

The moments on the floor beam are: 

Dead load nioment=10,800X4.82= 52,060 ft. lbs. 

Live load moment=80,000X4.82—385,600 ft. lbs. 
Economic depth from equation (10) (no flange plates) is 


1.52 



411600X12_ rr 
10000X% 


inches 


The depth assumed in the calculations for the depth of truss 
was about 13 inches more than the depth cf the stringer, or 
inches. (See Fig. 55). 


It is desirable to have the stringer connection come between 
the flange angled of the floor beam rather than to have it lap 
over the vertical legs of these angles, in order to dispense with 
filler plates under the conneetian angles. For these reasons then 
we will use a web plate 64 inches deep. 

The maximum shear=10,800-|-80,000=90,800 lbs. 

Using a %" web plate the unit shears— 800 —3780 lbs. per 

24 


sq. in., which is safe. 

Assuming that the flange angles will be 6"x6", the effective 
depth will be about 61 inches. 


Approx. D. L. flange stress= 
Approx. L. L. flange stress= 
Approx. D. L. required area= 
Approx. L. L. required area^= 


52060X 12 
61 

38560 0X12 
61 
10240 


=10,240 lbs. 
=75,860 lbs. 


20000 

75860 

10000 


-=0.52 sq. in. 
=7.59 sq. in. 


Total=8.11 sq. in. 

2 Ls 6"x6"x T y'=10.12—4XrVX 1=8.37 sq. in. net. {% 
inch rivets, no holes out of horizontol legs, two holes out of ver¬ 
tical legs, to comply with Spec. §64.) 

The actual effective depth=64.25—2X1.66=60.93 in. 

This will not change the flange stresses given above appre¬ 
ciably, so the flange as designed will answer. 













Art. 68. 


DESIGN OF FLOOR BEAMS. 


167 


There must be sufficient rivets through the flange angles 
and web to develop the entire flange stress between the end of 
the beam and the stringer connection. This will require more 
rivets than would be given by the horizontal increment (49) 
because the flange angles cannot run to the theoretical end of 
the beam which is at the center of the truss. 

End Floor Beams are required by §10 of the specifications, 
and it is always good practice to use them rather than to allow 
the end stringers to rest directly on the abutments. 

The end floor beam must carry the half panel load from the 
end panel of the bridge, and also the load from the short space 
between the end floor beam and the back wall, which is usually 
bridged by a cantilever bracket riveted to the beam opposite 
each stringer. This space will be about two feet in our case. 

The dead load at each stringer connection will be 
Floor (13.5+2.0)200=3100 lbs. 

Stringer 15.5X165=2560 lbs. 

Floor Beam say = 840 lbs. 


Total D. L.=6500 lbs. 

The live load reaction at the stringer connection must be 

determined from the actual 
wheel loads. The maximum 
reaction on the end floor 
beam will occur with the 
wheels placed as shown in 
Fig. 63. 

Fig. 68. 

The reaction at a=— 85 °- - =66,100 lbs. * 

27 

Dead load moment= 6,500X4-82= 31,300 ft. lbs. 

Live load moment=66,100X4.82=318,600 ft. lbs. 

In order to simplify the connection of the end floor beam to 
the truss, it should be made as shallow as is consistent. We will 
therefore make the depth only sufficient to allow the stringer to 
enter between the horizontal legs of the flange angles. This will 
require a depth of about 52% or 53 inches. 

We will use a web plate 53"x%". 



Unit shearing stress= 


72600 

19.87 


=3660 lbs. per sq. in., 


which is 


safe. 















168 


DESIGN OF FLOOR BEAMS. 


Art. 68. 


The effective depth will be about 51 inches. 

Approx. D. L. flange stress= 313 °^* — — 7,360 lbs. 


Approx. L. L. flange stress= 


51 

318600X12 


51 

7360 


75,000 lbs. 


Approx, required D. L. area=—-—- = 0.37 sq. in. 


Approx, required L. L. area= 


75000 

10000 


=7.50 sq. in. 


Total=7.87 sq. in. 

If the required rivet pitch (49) is not too small for a single 
line of rivets in the flange, we may use unequal legged angles 
for the flange with the long legs horizontal, which will be more 
economical. 


Try 2 Ls 6"x3y 2 "x%" Net area=9.00—2 X%X 1=8.00 
sq. in. (% inch rivets and no holes out of horizontal legs.) 

Actual effective depth=53.25—2X0.83=51.59. 

Actual D. L. flange stress= 3130 0 — 7,300 lbs. 

51.59 

Actual L. L. flange stress= 3 - 8 ^°^ 2 =74,100 lbs. 

7300 - 

Actual required D. L. area= -=0.37 sq. in. 

1 20000 

Actual required L. L. area= — - 00 =7.41 sq. in. 

1 10000 

Total=7.78 sq. in. 

This will not allow a reduction below the section assumed 
above. 

The number of rivets required to connect the flange angles 
to the web, between the stringer connection and the end of the 
beam will be the total flange stress 81,400 lbs. divided by the 
value of a y 8 " rivet in bearing on the %" web. (See Spec. §40). 

Number of rivets= 8 — - — =21. 

3938 

The distance from the stringer connection to the end of the 
beam will be about 3'-9". 

45 

Required rivet pitch=— =2.12 inches, which is less than 

12 

should be allowed in a single line (7). (Spec. §54). Therefore 














Art. 69. 


TOP LATERAL BRACING. 


169 


G^xG" angles must be used for the flange angles. 

Try 2Ls 6"x6"x r y'. Net area=10.12— 4X T VX 1=8*37 
sq. in. Actual effective depth=53.25—2X1-66=49.93 in. 

Actual D. L. flange stress= 31300 ^ 12 = 7,500 lbs. 

49.93 

Actual L. L. flange stress= 2 —76,600 lbs. 

49.93 

Actual required D. L. area= <5QQ -—0.38 sq. in. 

20000 1 

Actual required L. L. area=^^-= 7.66 sq. in. 

10000 _ 

Tota 1=8.04 sq. in. 

Use for flanges 2 Ls 6"x6"x T V'. 

69. Top Lateral Bracing. (59) The top lateral system 
is a horizontal Pratt truss of five panels, with the portals at the 
ends acting as abutments. 

Panel load of wind load for top lateral system=200X27= 

5400 lbs. Sec0==^^-=== 1.95. 

16.15 

The stresses are as follows: 

Diagonal #(7=2X5400X1.95=21,100 lbs. 

Diagonal CD =1X5400X1.95=10,600 lbs. 

Diagonal DD= 0 

Strut CC= iy 2 X5400=8.100 lbs. 

Strut DD= i/ 2 X5400=2,700 lbs. 


B C D O' C B' 



Required area for diagonal BC— ----- - =1.18 sq. in. 

18000 

To comply with specifications §11 the lateral bracing must 
be made of shapes capable of resisting compression. It is not 
good practice to use angles smaller than about 3i4"x3"x jV' for 
these laterals. The net area of one angle 3 1 / 4"x3"x 1 6 6 " =1.94— 
2X ! 5 6 Xl=1.32 sq. in., so that these angles will answer for all 
the diagonals. 




















170 


BOTTOM LATERAL BRACING. 


Art. 70. 


The size of the intermediate struts will be determined by 
§§35, 83 and 107 of the specifications. The unsupported length 
will be about 170 in. From Spec. §35 the least allowable radius 

of ffyration=——1.42 inches. This will require at least 

120 

2 Ls 3"x2%"x 1 5 6 ", which are also required to comply with §83 
of the specifications. 

Allowed unit stress=13,000—60—=6,000 lbs. per sq. in. 

r 

7> . T _ 8100 -j 

Required 'area=-=1.35 sq. in. 

1 6000 

Actual area=2X 1.63=3.26 sq. in. 

These top strut angles are run over the top chords and 
riveted -to the cover plates, and two other angles back to back 
are riveted between the intermediate posts as low down as the 
specified head room will allow (See Spec. §107). These two 
struts are connected by diagonal lattice work of angles similar 
to the portal (See Fig. 62). 

70. Bottom Lateral Bracing. The bottom lateral system 
(Fig. 64) must resist a static load of 150 lbs. per lin. ft. and a 
moving load of 450 lbs. per lin. ft. (Spec. §24.) 

Panel load D. L. wind=150X27= 4,050 lbs. 

Panel load L. L. wind=450X27=12,150 lbs. 
sec0= 1.95 (same as for top lateral system). 

The total stresses in the diagonals 'are as follows: 


o b c c/ c/' c‘ b a' 



Diag. a5=4050X3Xl-95+12,150X 3X1.95=94,700 lbs. 
Diag. 5c=4050X2X 1-95+12,150X l r X 1-95=66,500 lbs. 
Diag. cd=4050XlXl.95+12,150X 1 7 ° Xl.95=41,700 lbs. 
Diag. dd=4050X0Xl.95+12,150X f X 1.95=20,300 lbs. 


Required area a&= 
Required area bc= 


91700 

18000 

66500 


=5.26 sq. in. 
=3.70 sq. in. 


18000 




















Art 71. 


SHOES AND ROLLERS. 


171 


Required area cd— =2.32 sq. in. 

18000 1 

Required area dd'= 2 -^-= 1.13 sq. in. 

18000 

To comply with §33 of the specifications both legs of an 
angle in tension must be connected if the area of both legs is 
regarded as effective section, and therefore according to speci¬ 
fications §64 at least two holes must be deducted from the gross 
section of each angle. 

Use for diagonal ab 2 Ls 6"x3%"x%". Net area=6.86— 
4X%X 1=5.36 sq. in. 

Use for diagonal be 2 Ls 5"x3y 2 "x /g". Net area=5.12 — 
4X ^ X 1=3.87 sq. in. 

Use for diagonal cd 1 L 5"x4"x%". Net area=3.24—2X% 
X 1=2.49 sq. in. 

Use for diagonal dd' 1 L 3y 2 "x3"x , Net area=1.94— 

2X f^X 1=1.32 sq. in. 

The bottom flanges of the floor beams act as the bottom 
lateral struts, and the compression from the lateral forces tends 
to relive the tension in them from vertical loads. 

71. Shoes and Rollers. The end reaction will be 3 y 2 panel 
loads of D.L.+L.L =3y 2 X96,430=337,500 lbs. 

According to specifications §113 this will require 

-=13o0 sq. in. bearing on the masonry. 

250 

The masonry plate may be made say 3'-6" long by 33 inches 
wide, giving a bearing area of 1386 sq. in. According to speci¬ 
fications §114 the rollers cannot be made less than 5% inches in 
diameter. 

The maximum allowed pressure on the rollers will be 
300X5 3 4=1725 lbs. per lin. in. 

Required length of rollers— -- 7500 =196 inches. 

1725 

This might be made up of 6 rollers 33 inches long, or 7 rol¬ 
lers 28 inches long. The details can not be worked out without 
detailing the end posts, end floor beams and shoes. 

72. Estimate and Stress Sheet. The estimate of weight 
will now be given. The details can only be estimated approxi¬ 
mately until the detail drawings are made. Ordinarily the 






172 


ESTIMATE AND STRESS SHEET 


Art. 72. 


details are put in the estimate as a percentage of the main truss 
members, and an estimator of experience in detailing and es¬ 
timating can choose his percentages so that the total error in 
weight will be very small. 

The stress sheet may now be drawn up. (See Fig. 66.) 

This is usually as much ias is done until after the contract 
is awarded. The bridge company who fabricates the work 
makes the detail shop drawings, which are then approved by 
the railroad company’s engineer. 


rORM No. 1 


THE OHIO STATE BRIDGE COMPANY 

Sheet No. — 7 _ Made by ^-777/27^. _ Date _ 74. 

Estimate for_ ~jE? _ /Vo- /O/ - 5/^X4cT/V7 79/7 _ _ 


Span Extreme / 92 'iR/Sl 
Roadway^S"Z^£ Troo/c. 

Sidewalk_ SVoSfC _ 

Capacity Trusses _ . 

Capacity Flocri??^'^^ , ?^•. 
Spcclfications<^?o i gw-.-t ’06 


Span C. to C. _ //19:<2 _ 

y Panels at^Z^ l_ 

Depth C. to C. 32-0 _ 

Length of Diag. 46.8Z _ 

_ 7l7779 C- f*C: /<C /5_ _ 

isdri 


S< * ^ 


Estimated | | Steel_ /.9*±3_ 

DL per ft. ( ( Floor & Trac k j4.QP.. 

Total 2 

Panel Load per Truss DL s?/i2.^.^.. 
.LL . 


Total Steel 

Steel per ft. /&3&. 

Total Lumber_ 


c 


/ 

\ 

V / 

/ 

X 

/ 

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c/ O'’ C 


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Wt. 

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Length 

WEIGHT 








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$ 

124 

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for 

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$7+ 


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FORM No 2 


THE: OHIO STATE BRIDGE COMPANY 

Sheet No.-v3 _ _ Made by_ Date _ 

Estimate for- /Z&rJZJE. 3?JJ- _ /Sj'TP&pZL Afe.J(2£<P3>2 _ 


MEM 


OL 

Stress 


LL 

Stress 


Impact 


Total 

Stress 


Unit 

Stress 


Req. 

Area 


MATERIAL 


Actual 

Area 


No. 

Pcs. 


Wt. 
P. Ft. 


Length 


WEIGHT 


/L'''G$2A*2jL 






£.c/ 


jafc/.. 


?4i 


tjlo 


&26 


663 


4JZ 


Z&3 




4^ 


Cj2j 


'/?2L 


7 


i£/pjy£ 




Jt/fa 


SM 


3 . 7 * 




32 

7/3 


jLLs&sf*#- 

ZjL-^£<3£jS' 


JL 


78J 

-Z43L 


732 


/-36~-r 


J4kJ 


/✓ // 


££l?£... 


7-/2 • 


JL* 

_ 


/ 7 32*3"^ 


3. 

S_ 

■4 


772 


700 


47 
4.0 
6 a 


30.0 

30.0 


72 


453 


30,0 

4.0 


a 


7380 


SOP- 


w# 

Amp 


40, 


4 

2 


3.0 


23.8 


2> 


753 


7JL 


6 j£ 


£.0 
6*0 
/ a> 


f 


ZOO. 

'.4M 


go 


ff 




m 


Sir&h. 


JO. 


600 . 


Io/qtLcAplA 


U 32.2 3*j£- 


70 


jQ&AIoj/tAh/ 




■Szzz ?/dfa/A ippj 


320 




-Z67°0 


Tapy/ce /A 3 \2A. 


'■ JT 


2 QOZi'oo* 




irn 


32.0 

/2 


r* 


2L 


:40O 


^fe/T. TtzZ/i v/Al 7 jl 'Q 7a 


■4.7s 3-2AML 


jLs£& 4/7, 3^££l_ 




00 


4 


8403 


7nocA’ /jo/A 





'A 







































































































































































































Fig. 66 

































































CHAPTER VII. 

DETAILS OF PIN CONNECTED BRIDGES. 

The design of the bridge and stress sheet are usually worked 
out by the purchaser’s engineer and submitted to the prospective 
bidders for prices, but sometimes the bidders are asked to submit 
designs with their bids. (16) 

After the contract is awarded the detail shop drawings are 
made by the contractor and approved by the purchaser’s engi¬ 
neer. (See Chapter III.) These detail drawings show the sizes 
and positions of all connections and details of members, together 
with the number and location of all rivets. 

The details must be so proportioned that the stresses will 
be safely and economically transmitted from member to member 
and finally to the abutments. 

73. Pins. A pin is a beam which transmits the stresses at 
a joint. It is acted upon by forces in different planes, which 
produce bending moments and shears in it. 

It is usually convenient to resolve these forces into their 
vertical and horizontal components and get the bending moments 
in these two planes separately. The maximum bending moment 
at any point then is the resultant of the horizontal and vertical 
moments at that point. Likewise the maximum shear at any 
point is the resultant of the horizontal and vertical shears at the 
point. 

Since, in most cases, the maximum stresses in all of the 
members connecting to a pin do not occur under the same 
loading, the condition for a maximum moment in the pin is 
uncertain, and the moment must be calculated for the several 
conditions which give maximum stresses in the various members. 

In proportioning the pin for shear it must be remembered 
that the maximum intensity of shear on any cross section of a 
solid cylinder is equal to four thirds the average intensity. 1 

The bearing areas of the members on the pin must be suffi¬ 
cient so that the material will not crush. (10) On this account 
it is well to have large pins , because the larger the pin the less 
thickness of pin plates required, and also there will be less danger 

1 See Heller’s “Stresses in Structures,” Art. 71. Also Rankine’s 
Applied Mechanics, Art. 309. 


177 



178 


CALCULATION OF PINS. 


Art. 74. 


of unequal distribution of stress to the different parts of a mem¬ 
ber. For example, if there are four bars in a panel of the lower 
chord, they should be stressed in proportion to their areas, but 
this will not occur if the pin should bend so as to relieve some 
of the bars of stress. 

On the other hand, the larger the pins the larger will be 
the diameters of the evebar heads, and it is often difficult to find 
room for them, especially at the hip joint. 

The arrangement of the parts of the members on the pin is 
called the packing, and this should be such as to produce as small 
a moment as possible on the pin while at the same time insuring 
that the eye bars do not pull out of line in passing from joint to 
joint, more than about one-eighth of an inch per foot, and that 
the riveted members are of constant width throughout their 
length. 

The sizes of pins must be found h\j trial, since the moments 
depend upon the thicknesses of the bearings, and to get these we 
must first assume a diameter for the pin. 

74. Calculation of Pins. A few of the joints of the truss 
designed in Chapter YI will now be detailed to illustrate the 
methods. 

The Hip Joint. ( B ). According to §90 of the specifica¬ 
tions the least size of pin which may be used here is 0.8 X 6=4.8 
inches, or say 4% inches. 

The allowed bearing pressure on one linear inch of this pin 
is 4%X 12,500=60,940 lbs. for live loads and 121,880 lbs. for 
dead loads. (See Spec. §41.) 

Required bearing on end post aB 


DL— 

LL= 


123100 
121880 

255400 
60940 
Total=5.20 in. 


=1.01 in. 
=4.19 in. 


Required bearing on top chord BC 

132300 


DL= 

LL— 


121880 

274500 
60940 ’ 


1.09 in. 
4.50 in. 


Total=5.59 in. 








Art. 74 


CALCULATION OF PINS. 


179 


Required bearing on hip vertical Bb 

20900 


DL-- 


121880 


=0.17 in. 


t t _ 80100 - QO . 

LL=-—1.32 jn. 

60940 _ 


Total=1.49 in. 


The bearing* pressures on the eyebars of member Be is 
taken care of by complying with §90 of the specifications. 

With these bearing thicknesses the spacing of the forces 
acting on the pin may be determined approximately, as shown 
in Fig. 67. Sufficient clearance must be allowed between the 
different parts to allow them to be easily assembled. 


Fig. 67 shows a horizontal projection of the joint. In order 

to render the bending moment 
as small as possible (Spec. §90) 
the eye bars should be packed 
as near their insistences as pos¬ 
sible. 

The bending moments and 
• shears will have to be calculated 

for two positions of the live 
load, one which gives maximum 



Fig. 67. 

PACKING AT B. 

stresses in the top chord end post and hip vertical, and one which 
gives a maximum stress in the diagonal Be. 


The specifications §41 permits the calculation of the moments 
on the assumption that the pressures are uniformly distributed 
over the middle half of the bearing areas. The moments will be 
only slightly increased if we consider the forces as concentrated 
at the centers of the bearing areas, and this will greatly simplify 
the calculations. This assumption is usually made. 

The calculation of the moments is best made in tabular form, 
remembering that the moment at any force is equal to the 
moment at the next preceding force plus the product of the shear 
by the distance between the forces. 

In making up the table always begin at the outside where 
the shear is zero and work toward the center where the shear is 
again zero. 































180 


CALCULATION OF PINS. 


Art. 74. 


MAXIMUM STRESSES IN a B AND BC 


Mem. 

Be 

BC 

aB 

Be 

~Bb 


MOMENTS OF HORIZONTAL COMPONENTS. 


Horizontal 

Shear 

Lever Arm 

Moments 

Component 

in inches 

Increment 

Total 

— 40700 

40700 

9 

81400 


4-203400 


Li 

O ItOO 

81400 

+162700 

3 

4-122000 


1 99000 

4 

4- 40600 

J- 4kd jU\J\J\J 

4- 40700 

9 

4- 81400 

40700 

Li 

4-122000 

rkVJ 4 

000 

o 

000 

0U0 

2 

4-122000 


MOMENTS OF VERTICAL COMPONENTS. 


Shear 

Lever Arm 

in inches 

48200 

2 

48200 

i 

- 4-96400 

2 

+48'i00 

2 




Mem. 


Be 


BC 


aB 


Be 


Bb 


Vertical 
Component 


— 48200 


000 


-f-144600 


— 48200 


48200 


Moments 


Increment 


— 96400 


— 36150 


4-192800 


4- 96400 


Total 


96400 


132550 


4- 60250 


4-156650 


The maximum for this loading occurs at Bb and is 
j/(lz2uoo) 2 + (15G66U,2=198,730 in. lbs. 


MAXIMUM STRESS IN Be. 


MOMENTS OF HORIZONTAL COMPONENTS. 


Mem. 

Horizontal 

Component 

Be 

— 42800 

BC 

4-184100 

aB 

— 98500 

Be 

— 42800 

Bb 

000 


Shear 

Lever Arm 
in inches 

Moments 

Increment 

Total 

42800 

2 

— 85600 



.+ 41820 

i 

+ 106000 

oODUU 

4- 20400 

-+ 42 v 00 

2 

4- 85600 

4-106000 

000 

2 

000 


4-106000 


























































































































Art. 74. 


CALCULATION OF PINS. 


181 


MOMENTS OF VERTICAL COMPONENTS. 


Mem. 

Vertical 

Components 

Shear 

Lever Arm 
in inches 

Moments 

Increment 

Total 

Be 

— 50500 


2 

—101000 

—101000 

BC 

— 000 

— OUDUU 


KACAA 

f 

— 37800 

—138800 

aB 

+116500 

—ououu 

+66000 

2 

+132000 

— 6800 

Be 

— 50500 

+15500 

2 

+ 31000 

+ 24200 

Bb 

— 15500 


The maximum resultant moment for this loading occurs at 
aB and is i/(20400) 2 + (138800) 2 =140,300 in. lbs. 

Then the maximum bending moment on the pin occurs 
under full loading and is 198,700 in. lbs. 

With an allowed fiber stress of 18,000 lbs. per sq. in. this 
will require a 47(s inch pin, (see Cambria, page 312), or exactly 
the size that was assumed. 


The maximum shear occurs for full load between members 
BC and aB, and is |/(l62700) 2 +(48200) 2 =170,000 lbs. 

This gives a maximum unit shear of =12150 lbs. 

3X18.66 

per sq. in. 

The specifications only allows a unit shear of 9000 lbs. per 
sq. in. (see §41) so the size must be increased. This will not 
change the shears in any way, but will change the required bear¬ 
ing areas and lever arms and moments. 


Required area for shea 


4X170000 

3X9000 


=25.2 sq .in. 


A 5% inch pin will answer. 

In a similar manner the pins at the other joints are figured 
with the following results: 

At a a 5% inch pin is required. 

At c a 5y 2 inch pin is required. 

At d a 5% inch pin is required. 


It will make the shop work somewhat less if these pins are 
all made the same size, so we will use 5% inch pins at a, c, d 
and B. 














































182 


RIVETED TENSION MEMBER. 


Art. 75. 


No pin is used at b, but the bottom chord is run through 
continuous from a to c, and a riveted connection is made at b 
between Bb and the chord abc. 

■At C a 4% inch pin is required, and we will use the same 
size at D. 


Figures 68 to 71, inclusive, show the packing at the various 
joints. 




75. Details of a Riveted Tension Member. (11) A detail 

drawing of one end of the lower chord abc is shown in Fig. 72. 
The width of the member is determined by the packing at a -and c 
as shown in Figs. 68 and 69. 


















































































































































Art. 76. 


RIVETED TENSION MEMBER. 


183 


The maximum stress in the member is 345,900 lbs. (. DL+LL 
-f-Wind). Ihe average allowed unit stress in tension is 15,520 
lbs. per sq. in., and the required net area of the body of the 
member is 22.29 sq. in. (See Art. 64.) According to the speci¬ 
fications §68 the net section through the pin hole must be one- 
third in excess of this amount, or 29.72 sq. in., and the least 
section back of the pin hole 60% of this, or 17.83 sq. in. 

34ie net section of the 2—14"X%" plates through the pin 
hole is 

2(2X2i/ 8 +2 ,/ (2 i/ 2 )-+ (4%2)%=5.60 sq. in. 

The balance 29. 1 2 5.60=24.12 sq. in., must be made up 
of pin plates. 

The effective net width through the pin hole of piates 16 
inches wide is (See Fig. 72) 



(2X3%+2 1 /( 2 %)s+(4%)a-5%—2)==9.46 in. 

Then the required thickness for pin plates 16 inches wide 
to take the tension is 

24 12 

— : —=2.55 in., or say 2% inches. 

9.46 J 

This will require two pin plates on each side 16"x%". 

The average allowed unit stress in bearing on the pin 






































































184 


RIVETED TENSION MEMBER. 


Art. 75. 


(DL-\-LL-\-W )=— r - X l-3=19,400 lbs. per sq. in. (From 

ui 4. O 

1 + 406TF 

Eq. (21) and Spec. §39), and the allowed bearing pressure per 
linear inch of pin is 5% X 19400=111,550 lbs. 

None of the bearing plates can however be counted on to 
take more stress in bearing than they transmit past the pin hole 
in tension. 

The stress transmitted by the 2—14"X%' r plates past the 


pin hole will be proportional to the areas, and 


is-^- x 345,900= 
29.25 


66,200 lbs. 

The stress transmitted by the other pin plates is 345,900— 
66,200=279,700 lbs. 

Then the required bearing thickness of the 16 inch pin 


plates= 2797 -° =2.5 inches, therefore the 2 — 16"X% // plates on 

111550 * 

each side are sufficient. 


The required net length back of the pin hole= 


17.83 

3.25 


=5.5 in. 


Allowing one rivet hole out this will requrie the pin plates to 
extend 5 1 / 4-f-l+2''/ s =9% inches beyond the pin center. 


The stresses taken by the component parts of the body of 
the member will be in proportion to their gross areas because 
their deformations must be equal, and the connection must dis¬ 
tribute this stress properly to the component parts. 

The stress taken in the body of the member by 1—14"X%'' 


plate= 


5.25 

28.50 


x 345,900=63,700 


lbs. 


The stress transmitted past the pin hole by each of the 
16"X% /r pin plates=i4X279,700=69,980 lbs., and sufficient 
rivets must be provided to transmit this stress from the pin 
plates to the body of the member. 

The six countersunk rivets between the pin and the end of 
the angles may be considered as transmitting stress from the 
outside pin plate to the 14"X%" plate so long as this does not 
raise the total stress in that plate beyond 63,700 lbs. 

The value of the six countersunk rivets in the % inch plate 
Is 6X f X4,922=12,660 lbs. (Spec., §40.) This would bring 
the total stress in the 14"X%" plate at the end of the angles 










Art 76. TOP CHORD AND END POSTS. 185 


up to 12.660+34 (66200)=45,760 lbs., which is less than 63,700 
lbs/, and therefore safe. 

Further rivets will be required in the outside pin plate to 
transmit 69,980—12,660=57,320 lbs. The rivets will be in single 

shear and the number required= — 320 =11. 

6412 

'The rivets to transmit the stress from the inside 16"X% ,/ 
pin plate must be placed beyond those required for the outside 


pin plate. 


The number required= 


69980 _ 
5412 “ 


The required net area of the body of the member through 
the first line of rivets of the connection plates is 22.29 sq. in., 
and the required net area on a zig zag line of holes=l.3X22.29 
=28.98 sq. in. (Spec. §64.) 

Assuming that a lacing rivet comes opposite the first rivet 
in the pin plate (which is not exactly the case here) we may 
write an equation as follows, and solve for the least allowable 
pitch of rivets in the connection plate at this point. (11). 


Calling this distance x we have 


28.98=y 2 X4(l 1 / 2 +l 1 /2+v / (2y 4 y+x 2 +V / (S%y+x ’-—3 ) 
+2X% ( 2%+2i4+5i4+2 j/(214) 2 -J-x 2 —4 ) 

Solving we get x=Sy 2 inches. 


This pitch may safely be reduced to 3 inches after the first 
line of rivets is passed, as the stress in the body of the member 
has been reduced by the value of the rivets passed. 

The lacing of a tension member does not have to comply 
with §97 of the specifications, and may be put in according to 
the judgment of the engineer. 

76. Location of Pins in Top Chord and End Posts. (58). 
The location of the pins in the top chords and end posts depends 
upon the location of the centers of gravity of the sections and 
upon the amount of the displacement of the pins necessary to 
compensate for the bending due to the weight of the member. 

The pin at the hip cannot be placed in the exact theoretical 
location for both the end post and top chord, and its location 
must necessarily be a compromise between the two. 











186 TOP CHORD AND END POSTS. Art. 76. 

Figure 73 shows the fac¬ 
tors which must be taken into 
consideration in this problem. 
From §43 of the specifications 
we see that the bending: mo¬ 
ment due to the weight of the 
member need not be consid¬ 
ered unless it increases the 
fiber stress more than 10% 
above the allowed unit. 

The weight of the end post wall be as follows: 

1 Cover plate 24"x%" 51.0 

2 Web plates 21"x%" 89.2 

2 Side plates 15"x%" 63.8 

2 Top Ls 3"x3"x%" 23.0 
2 Bottom Ls 4"x3"x%" 27.2 

254.2 

Details sav 10%= 25.8 

Total=280.0 lbs. per lin. ft. , 
The weight per linear foot horizontal will be 280 sin0=180 
lbs., and the bending moment due to the weight will be 

18OX272 =l 6 ,400 ft. lbs. 

8 

The maximum compressive fiber stress due to weight 

=-=400 lbs. per sq. m. m the top ot the cover 

4698 

plate. The allowed unit stress for DL-\-LL is 6516 lbs. per sq. 
in., therefore the bending moment due to weight need not be 
considered in the end post. 

The maximum compressive fiber stress due to weight or to 
displacement of the pins may reach 651 lbs. per sq. in. 

The weight of the end section of the top chord is as follows: 

1 Cover plate 24"x 1 /o // 40.8 

2 Web plates 18"x 68.8 

2 Top Ls 3"x3"x%" 14.4 
2 Bottom Ls 4"x3"x T6 " 24.8 

148.8 

Details say 10%= 14.2 



163.0 lbs. per ft. 












I 




Art. 77. 


LACING. 


187 


The bending* moment due to the weight = 1 ~ 3 x 27 2 == i4 «80 

<6 

ft. lbs. The distance from the middle of the web to the center 
of gravity is 1.98 in., and the moment of inertia about the hori¬ 
zontal axis is 2230. 

The maximum compressive fiber stress due to weight= 


14880X12X7.64 


2230 


=612 lbs. per sq. in. 


r l he average allowed unit stress for DL-\-LL from equation 
(21) is 9490 lbs. per sq. in., therefore the bending due to weight 
need not be considered in the top chord. 

The most desirable location for the pin will be obtained 
from equation (20) as follows: 

For the end post e— 1 ? - ^ 27 =0.42 in. 


For the top chord e= 


10X378500 
163X27 2 X12 


=0.36 in. 


10X406800 

For the end post the pin should be 1.77—0.42=1.35 in. 
above the center line of the web. 

For the top chord the pin should be 1.98—0.36=1.62 in. 
above the center line of the web. 

If x 2 in Fig. 73 is made 8 in. to agree with the most desirable 
position for the top chord, from similar triangles x x : x 2 =d x : d 2 
or r 1 =9.33 in., which would place the pin in the end post above 
the center of gravity. 

If x x is made 9*4 in. to agree with the most desirable posi¬ 
tion for the end post, r t ,=8.14 in. 

This will place the pin 1% in. above the center of the web 
of the end post and l l /o in. above the center of the web of the top 
chord. This location will be used. 

The pins at the intermediate top chord points are placed on 
the same center lines at those at the hips, as they only have to 
transmit the increments of stress from the diagonals. 

Figure 74 is a detail of the hip joint. 

77. Lacing of Compression Members. (58). For the top 

chord CD (which is the largest) the allowed unit stress for 

L 

20000—90 — T 

DL -(- LL from equation (21) is -— ; 940—53.7 " 


1.675 ' r 

9,920 lbs. per sq. in. (using the radius of gyration about the 

vertical axis.) 










188. 


LACING. 


Art. 77. 


'<?/7 /ro/ea 0/7 


/fojkj /&/ /^?sj6s/ C0/r/rec//<e77 



Fig. 74. 


From equation (18) 



4 X 19.93 X 20 
27X12 


= 497 lbs. 


per inch. 


Length of member covered by one lace bar (single lacing, 
Spec. §97)=22 1 / 4 cot. 60°=12.8 in. 

Longitudinal increment of stress taken by one bar=497x 
12.8X%—3180 lbs. (Half is taken by cover plate.) 



















































Art. 77. 


LACING. 


189 


Stress in one bar=3180 sec. 60°=6360 lbs. 

In the lattice it is safe to use the unit stresses allowed for 
lateral bracing. 

Specifications §97 requires the lattice for this chord to bo 
% in. thick. 

Allowed unit stress in compression is 


13000-60 


Required area= 


=13000- 

6360 


60X25.6 


Required widths 


4520 

1.41 

.625 


0.181 
=1.41 sq. in. 

=2.26 in. 


=4520 lbs. per sq. in. 


Use lace bars 3"x%" for top chords to comply with speci¬ 
fications §97. 

The lacing for the end posts cannot be obtained directly 
from equation (18) because the end post carries transverse shear 
in addition to the direct stress. 

The total difference in extreme fiber stress due to column 
action is obtained from the column formula for DL-\-LL-{- Wind. 
From Ecp (21) 

L 

L 


17000—90 


X 1-3=13,200—69.8 


> c 1.675 r 

The values of L and r here must be taken about a vertical 
axis because we are figuring for the shear in that direction. 

The difference in unit stresses due to column action=69.8X 

34X12 


8.68 


=3280 lbs. per sq. in. 


The difference in unit stresses due to transverse bending 
from Art. 66 = 3310 lbs. per sq. in. 

Total difference=3310-}-3280=6590 lbs. per sq. in. 

Total stress to be transferred by the lacing and cover plate 
in a distance of 17 ft. (distance from end to point of contra- 
flexure) =6590 X^4i=6590 X35.1=231,300 lbs. 

/=- =1134 lbs. per inch. 

17X12 

Longitudinal increment of stress taken by one bar=1134X 
12.8X^2—7260 lbs. 

Total stress in one bar=7260 sec. 60°=14,520 lbs. 













190 


LACING. 


Art. 77. 


Using bars % in. thick, the allowed compressive unit stress 
is 4520 lbs. per sq. in. 

Required area— —3.21 sq. in. 

4520 


Required width— --- 2 - =5.12 in. 

.625 

Use lace bars 5"x%" with two rivets in each end. 


For the intemiediate posts Cc, the radius of gyration per¬ 
pendicular to the channel webs is 4.31 in., and the unsupported 
length in that direction about 21 ft. 

The allowed unit stress for DL-\-LL= 10,060—53.25 — 

(See Art. 65) =6950 lbs. per sq. in. 

From equation (18) we get 


f~- 


4X11.76X3110 


=580 lbs. per inch. 


21X12 

The length covered by one lace bar (single lacing, Spec, 
is 3 y 2 inches. 


197) 


Longitudinal increment of stress taken by one bar=580 X 
3 i/ 2 XMr-1015 lbs. (Lacing on two sides.) 

Stress in one bar=1015 sec. 60°=2030 lbs. 

Specifications §97 requires that the lacing for this case be- 4 7 0 - 
inches thick, but §82 limits us to % in. 

Allowed unit stress=13000 — 60 ^ —=9100 lbs. per sq. in. 

.108 11 


2030 

Required area^=—-— =0.23 sq. in. 

9100 

Required widt'h=-2^—=0.61 in. 

.375 

Specifications §97 requires 2M> in. X % in. 

For post Dd specifications requires lacing 2 1 / 4'b 


78. Details of the Floor Beams. Figure 75 shows a detail 
drawing of one of the intermediate floor beams. Cooper’s speci¬ 
fications requires the use of a number of different unit stresses 
for rivets in various positions, and these must be kept in mind. 
(§40) 

Rivets required for stringer connection= — 00 =35. 

2625 












Art. 78. 


FLOOR BEAMS. 


191 


Rivets Required for end connection angles through web 

90800 

8659 


90800 

Rivets required for end connection to post=-=32. 

2886 

86100 

Rivets required for connection of flanges to web=-=23. 

3938 

(Shop rivets in bearing on % in. web.) 

At the end of the bottom flange the expedient is resorted 
to of riveting a plate on top of the angles to transfer a part of 
the stress to the web. This then gives us the following value: 

16 rivets bearing on % in. web=16X3938= 63,000 lbs. 

6 rivets double shear = 6 >'8659= 51,900 lbs. 


The top flange has 26 rivets effective. 


Rivets required for web splice 


90800 

3938 


=23. 


114,900 lbs. 








\ 


Fig. 75 
















































































































INDEX 


Art. Page 

Adding machines . 18 37 

Angles—maximum lengths . 52 124 

Bearing plates if or plate girder. 52 132 

Bending of chords due to weight . 58 145 

Bolsters for plate girder . 52 132 

Books of reference . 25 50 

Bottom lateral bracing . 70 170 

Bex girders . 42 99 

Building construction . 37 80 

Built tension members . 57 141 

tension members . 64 152 

Butt joints .✓. 8 12 

Button head rivets . 1 1 

Calculation of pins . 74 178 

Center of gravity. 65 157 

Choirds—Design of . 65 156 

—Location of pins . 76 185 

Classes of structural steel work... 14 29 

Clearances . 27 60 

Columns . 58 142 

Compression and bending combined. 58 144 

Compression members . 58 142 

—Allowance for rivet holes... 4 5 

—Design of . 65 154 

—Width of . 65 155 

Contracts and proposals . 16 30 

Corrugated iron or steel . 35 77 

Countersunk rivets . 1 1 

Countersunk rivet values . 6 15 

Dead load . 61 147 

for plate girder bridge . 52 116 

of truss bridges . 56 141 

Dead loads—Roof . 40 86 

Deck plate girder bridge design . 52 115 

estimate . 52 134 

stress sheet . 52 136 

Depth of truss . 62 147 

Depth of trusses . 55 139 

10 s 








































194 


INDEX. 


Design of chords . 

compression members . 

end posts . 

deck plate girder bridge ... 

floor beam . 

pin-connected bridge . 

portal . 

riveted connections . 

a roof . 

a stringer . 

tension members . 

Designing and estimating . 

Designing and estimating . 

Details—Duplication of . 

floor beams . 

hip joint . 

pin connected bridges . 

a riveted tension member. . 

Dolly . 

Drafting department .u ... 

Draftsman’s equipment . 

Drawing boards . 

instruments . 

pencils . 

room light . 

table ..i 

Drawings for roof trusses . 

Drawing oif roof truss . 

Drift pins . 

Driving rivets . 

Eccentricity of pins in cthord members 

Economic depth of girders . 

girders . 

girders . 

trusses . 

Effective depth of plate girders . 

End floor beam . 

End posts—Design of . 

—Lacing . 

Equivalent loads ... 

Erection . 

Erection and manufacture . 

Estimate for deck plate girder bridge 
for pin connected bridge . .. 

of weight of stringers. 

Estimates of cost. 

Estimates—-Forms of . 


Art. 

Page 

65 

156 

65 

154 

66 

159 

52 

115 

68 

165 

60 

146 

67 

163 

9 

13 

40 

81 

51 • 

110 

64 

150 

17 

31 

Chap. II 

29 

27 

58 

78 

190 

76 

188 

Chap. VII 

177 

75 

182 

o 

o 

4 

24 

46 

25 

47 

24 

47 

25 

48 

25 

49 

24 

47 

24 

47 

41 

91 

• a 

98 

2 

3 

O 

6 

3 

58 

145 

46 

103 

-51 

111 

52 

119 

55 

139 

45 

103 

68 

167 

66 

159 

77 

189 

56 

140 

23 

45 

Chap. Ill 

44 

52 

134 

72 

173 

51 

115 

17 

31 

17 • 

33 

















































INDEX 


195 

Art. Page 

Estimating and designing . 17 31 

and designing .Chap. II 29 

—Order of . 19 37 

—Order for highway bridges . 19 39 

—Order for railway bridges . 19 38 

•—Order for steel buildings . 19 40 

Eye bars . 57 141 

False work .;. 23 45 

Field riveting . 23 46 

Field rivet values . 9 14 

Flange plates of plate girders. 52 121 

riveting in plate girders . 49 107 

riveting in plate girders . 51 113 

riveting in plate girders . 52 122 

sections . 42 99 

splices in plate girders . 5'0 110 

splices in plate girders . 52 124 

Flanges of girders . 45 102 

girders . 51 112 

girders . 52 120 

Floor beams—Details . 78 190 

—Details . 78 192 

—Design . 68 165 

Floor—Design of, for bridge . 52 115 

Freight . 31 69 

Gallows frame . 23 45 

General plans . 21 42 

Girders .Chap. V 99 

—Economic depth . 46 103 

v —Effective depth . 45 103 

—The flanges . 45 102 

—^Flange riveting . 48 107 

—Flange splices . 50 110 

—Maximum lengths f . 42 99 

—Moment of resistance. 43 99 

—Shear distribution . 44 100 

—Stiffeners . 47 105 

—Stresses . 43 99 

—Stresses . 54 

—Stresses . 52 117 

—The web . 44 100 

—Web splices . 48 406 

Grip of rivets . 1 

Heating rivets. 

Hip joint—Detail of .'•. 76 

pin . 74 178 

Inertia—Moment of . 65 108 

















































196 


INDEX. 


Art. Page 

Inspection ./. 33 75 

Intermediate posts—Lacing . 77 190 

Jack rafters. 37 80 

Joints—Butt . 8 12 

—Lap . 8 12 

Lacing of compression members . 58 143 

compression members .■. 77 187 

Lap joints . 8 12 

Laterals—Bottom . 70 170 

Lateral bracing of plate girders . 52 127 

stringers . 61 114 

Lateral systems . 59 146 

Laterals—Top . 69 169 

Loads . 56 140 

Loads 1 —Roof . 38 81 

Location of pins in top chord and end posts. 76 185 

Manufacture and erection .Chap. Ill 44 

Materials . 32 70 

Material orders . 26 51 

Moment in deck plate girder . 52 117 

Moment of inertia . 65 158 

Moment of resistance of plate girder. 43 100 

Net sections of tension members . 11 20 

Order of estimating . 19 37 

highway bridges . 19 39 

railway bridges . 19 38 

steel buildings . 19 40 

Order of procedure for a ,pin connected bridge. 28 62 

for plate girder bridge . 29 65 

Ordering material . 26 51 

Packing . 73 178 

Packing at various joints . 74 182 

Panel lengths . 55 139 

Pins . 73' 177 

Pins—Calculation . 74 178 

Pin-connected bridges .Chap. VI 139 

—Design of . 60 146 

details .Chap. VII 177 

—'Estimate . 72 173 

—Order of procedure for. 28 62 

stresses . 63 148 

—(Stress sheet . 72 176 

Pins—Location in top chord and end posts. 76 185 

Pin plates . 10 16 

Pin plates .*. 10 18 

Pitch of rivets defined . 7 10 

Pitch of roofs . 35 78 

















































INDEX. 


Plans—General . 

Plans—Show . 

Plate girder bridges . 

Plate girder bridge—Order of procedure . 

Plate girder design . . . 

Plate girders—Economic depth . 

—Economic depth . 

—Economic depth . 

—Effective depth . 

—Effective depth . 

—Effective depth . 

—Flanges . 

•—Flanges . 

—Flanges . 

—Flange plates . 

—Flange riveting . 

—Flange riveting . 

—Flange riveting . 

—Flange splices . 

—Flange splices . 

—Lateral bracing . 

—Maximum moment . 

—Stiffeners . 

—Stiffeners . 

—Stiffeners . 

—Stresses . 

—Stresses . 

'—Stresses . 

—Web . 

—Web . 

—Web . 

—Web splices . 

—Web splices . 

Plates—Sizes of... 

Pony trusses .. 

Portal bracing . 

Proposals and contracts . 

Purlins . 

Radius of gyration . 

Rafter design, for a roof truss . 

Reaming . 

Rivet holes . 

—Allowance for in compression members 

in tension members . 

Rivet pitch in flanges of girders . 

Rivet spacing . 

Riveted joints—Alternating stresses .. 



197 

Art. 

Page 

21 

42 

21 

43 

Chap. V 

99 

29 

65 

52 

115 

46 

103 

51 

111 

52 

119 

45 

103 

51 

112 

52 

120 

45 

102 

51 

112 

52 

120 

52 

121 

49 

107 

51 

113 

52 

122 

50 

11'.) 

52 

124 

52 

127 

52 

117 

47 

105 

51 

114 

52 

124 

43 

99 

51 

112 

52 

117 

44 

100 

51 

111 

52 

120 

48 

106 

52 

120 

26 

53 

55 

140 

67 

163 

16 

30 

40 

86 

6i5 

157 

40 

88 

2 

2 

2 

2 

4 

5 

11 

20 

49 

107 

27 

59 

4 

7 
















































198 


INDEX. 


Riveted joints—Alternating stresses . 

—Assumption made in design of 

—Design of ..*. 

—Examples . 

—Friction in . 

—Kinds of . 

—Manner of failure . 

—Requirements for good . 

—Slip in . 

Riveted tension member details . 

Riveted truss bridges . 

Riveting . 

—Chain . 

—Design of joints in a roof truss. 

of flanges of plate girders. 

of flanges of plate girders. 

of flanges of plate girders. 

machines ... 

of pin plates . 

of pin plates . 

—;S tagger ed . 

—Theory of .. 

Rivets—American Bridge Company’s standard 

—Bending in . 

—‘Button heads .... 

—Conventional signs for . 

—Countersunk . 

—•Dimensions of . 

—Driving . 

—Field values . 

—Crip . 

—Heating .. 

—Initial tension in . 

—Length required .... 

.—Shape of heads . 

—Proper sizes .*. 

.—Spacing of . 

—Values of countersunk .. 

—Working stresses .. 

Rollers . 

Roofs . 

construction .. 

coverings . 

—Dead load . 

—Design of a .:. 

loads . 

pitch for various coverings . 


Art. 

5 

4 

9 

10 

4 
8 
9 

5 
4 

75 

28 

Chap. I 
9 
41 
49 

51 

52 

3 

10 

10 

9 

4 
1 
4 
1 

13 

1 

1 

9 

O 

9 

• 1 

9 

O 

4 

1 

1 

6 
r? 

i 

9 

9 

71 

Chap. IV 

34 

35 
40 
40 
38 
35 


Page 

9 

5 
13 

15 

6 

12 

13 

9 

6 

182 

64 

1 

13 

93 

107 

113 

122 

3 

16 
18 

13 

4 

1 

rr 

• i 
1 

28 

1 

1 

3 

14 
1 

4 
6 
2 
1 
9 

10 

15 
14 

171 

rr r+ 

i ( 

77 

77 
86 
84 
81 

78 

















































INDEX. 


Roof purlins . 

truss drawings . 

truss drawing . 

trusses—Types of . 

Scales .. *.. 

for roof truss drawing . 

for shop drawing . 

Shear—Distribution over cross section of girder.... 

Shear in girders .... 

Shear in girders . 

Shear in girders . 

Shipment .. 

Shoes for plate girder . 

Shoes and rollers . 

Shop bills . 

Shop drawings . 

drawings—'Methods of working up . 

drawings—Notes on . 

drawings for roof truss . 

drawings for roof truss . 

drawings—Titles on . 

Shop operations . 

Shops—Kinds of . 

Show plans . 

Signs for rivets on drawings . 

Sizes of rivets ... 

Sizes of rivets . 

Slide rules . 

—Duplex . 

—Engineer’s . 

—Fuller’s . 

—Manheim . 

—Rule for operation of. 

—Thacher’s . 

—Three multiple . 

Snap for rivet heads . 

Snow loads .. 

Solid floors . 

Spacing of rivets . 

Specifications . 

Splices in flanges of plate girders. 

—Elangeis of girders . 

in webs of plate girders. 

in webs of plate girders. 

Steel—Acid . 

—Basic . 

—Bessemer . 


Art. 

199 

Page 

40 

86 

41 

91 

41 

98 

36 

78 

25 

49 

41 

92 

28 

63 

44 

100 

44 

100 

51 

111 

6*2 

118 

31 

69 

52 

132 

71 

171 

30 

67 

27 

54 

27 

61 

27 

58 

41 

91 

41 

98 

27 

56 

22 

44 

15 

30 

21 

43 

13 

28 

1 

1 

6 

9 

18 

35 

18 

36 

18 

36 

18 

35 

18 

35 

18 

36 

16 

35 

18 

36 

O 

o 

4 

38 

83 

53 

138 

7 

10 

20 

41 

52 

124 

50 

110 

48 

106 

52 

125 

32 

72 

32 

72 

32 

71 
















































200 


INDEX. 


Art. Page 

Steel—Effect of carbon . 32 - 71 

—Open hearth . 32 72 

—Physical characteristics . 32 70 

—Process of manufacture . 32 71 

—'Specifications for . 32 70 

—Tests of . 3>2 74 

Stiffeners . 29 65 

Stiffeners . 47 1’05 

Stiffeners . 51 114 

Stiffeners . '52 124 

Stiffeners—Crimped . 47 105 

Stress sheets . 21 42 

for deck plate girder bridge. 52 136 

for pin connected bridge . 72 176 

for a roof . 40 90 

Stresses in girders . 43 99 

in girders . 51 112 

in girders . 52 117 

in pin connected bridge . 63 148 

in roof trusses . 39 84 

in roof trusses . 40 87 

in trusses of bridge due to wind. 63 149 

Stringer—Design . 51 110 

—Estimate of weight . 51 115 

laterals . 51 114 

Structural steel—Classes of . 14 29 

Templets . 22 44 

Tension members . 57 141 

—Euilt . 64 152 

—'Details of riveted . 75 182 

—Design of . 64 150 

—Net sections . 11 20 

Tension on rivet heads . 4 6 

Tests of steel . 32 74 

Theory of riveting . 4 4 

Through plate girders . 53 137 

Ties—Design of for bridge . 52 115 

Time savers . 18 35 

Titles on shop drawings . 27 56 

Top chord—Lacing . 77 187 

Top lateral bracing . 69 169 

Tracing linen . 27 54 

Traveler . 23 45 

Trusses—Types of . 55 139 

Types of plate girder flanges . 42 99 

Types of roof trusses . 36 78 

Types of trusses . 55 139 

















































INDEX. 


201 


Art. Page 

Webs of Girders. 44 100 

of girders . 51 111 

of girders . 52 120 

—Moment of resistance . 44 101 

—Moment of resistance . 45 102 

splices in plate girders. 48 106 

splices in plate girders . 52 125 

Width of compression members . 65 155 

Wind pressure . 38 82 


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( 



































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































